I think it is very important for Catholic Christians to evangelize separated Christians as well as non-Christians.

Jorge Bergoglio would condemn you for this.  Bergoglio's definition of "evangelization" positively precludes attempting to convert, which he calls "prosletyzing".

Jorge Bergoglio would condemn you for this.  Bergoglio's definition of "evangelization" positively precludes attempting to convert, which he calls "prosletyzing".

In my daughter's school I was asked to stop proposing why our Faith is so beautiful to fathers who have strayed because of spiritual indolence (which I am guilty of, too). I was formally asked by the school to stop proselytizing as our (their) faith is all inclusive and we welcome individuals of any (no) religious belief.

... my daughter's school is run by Opus Dei.

I undertook this oath, fully aware of its consequences and perfectly conscious of its implications.

How can a man's bond be invalid and not binding?

Lad is right, they cannot ask you that and you could not make that promise.

You said: "Finally I was asked to promise that I would never try to convert my wife, nor even pray for her conversion. I underline that it was not my wife who asked me to promise not to try to convert her, but the Orthodox clergymen.

I agreed and promised and we were dispenced and authorized to get married..."

First off, the Orthodox are in schism, that reason alone dictates that any dispensation from them is altogether worthless. The only reason you sought a dispensation was because your wife wanted one, not because you needed one from them.

Second, you could not licitly make that promise because in mixed marriages, the Church expects the Catholic spouse to work at converting the other one aka Cor 7:14 "For the unbelieving husband is sanctified by the believing wife; and the unbelieving wife is sanctified by the believing husband: otherwise your children should be unclean; but now they are holy."

What this all means is, they did wrong by asking you to make that promise and you did wrong to make that promise. You cannot be bound by a promise you could not make to begin with. Now it's time to correct yourself and pray for your wife's conversion!  

I undertook this oath, fully aware of its consequences and perfectly conscious of its implications.

How can a man's bond be invalid and not binding?

That's because they had no right to demand this off you.  Period.  It's like the case of people who makes these private vows effectively "selling their souls" to the devil.  Those are not binding, and as soon as the person changes his mind, the promise is broken ... that's because Our Lord through his Redemption has the rights over every soul.

If someone demands that you take an oath to kill someone, and you take the oath, you are under no obligation to follow through.  You sinned in taking the oath in the first place and need to confess it, but you are obliged before God in this case to break the oath, since it's invalid.  Same thing applies here.  You are not only ALLOWED to break this oath, you are absolutely required to and MUST pray for and work for the conversion of your wife.  Ask any Traditional Catholic priest and he'll tell you the same thing.  You are NOT bound by this oath, and in fact have an obligation to BREAK the oath, just as you would have an obligation to break your oath to murder someone.  Simply confess the fact that you made this oath in the first place, but other than that there's absolutely nothing to this oath.

If you were to take the solemn oaths of the Freemasons, for instance, you would not before God (and therefore objectively) be bound by them.  In fact, you'd be obliged to break them.

Dear Ascanio, I will surely pray for her conversion and salvation. Continue to love God, and love your wife. As others have said, schismatics have no jurisdiction, and do not have the right to demand oaths contrary to the Catholic Faith from you. But my opinion is you don't need to worry too much about any of that, for now,  just in your heart, offer to God abundant prayers and supplications for the conversion and salvation of your beloved wife. You need have no undue scruple about doing that. 

Consult a Traditional Catholic Priest on the subject when you can; and then God through him will lead you as to what you are to do beyond that point. 

Our Lady of Fatima has promised the conversion of Russia and the return of the Orthodox to the Roman Catholic Church when that country is Consecrated to the Immaculate Heart by the Pope and the Bishops. Hopefully, we will all live to see that happy day! God only accepts and approves of working for their conversion.

Jorge Bergoglio would condemn you for this.  Bergoglio's definition of "evangelization" positively precludes attempting to convert, which he calls "prosletyzing".

It shocked me when I first read this, but yeah, you're possibly right. Although some would distinguish the two. Anyway, an instruction on the Holy Office from the same: https://www.ewtn.com/catholicism/library/on-the-ecuмenical-movement-2070

The instruction on working authentically for "the only true union by the return of the dissidents to the one true Church of Christ" from H.H. Pope Pius XII: Therefore the <whole> and <entire> Catholic doctrine is to be presented and explained: by no means is it permitted to pass over in silence or to veil in ambiguous terms the Catholic truth regarding the nature and way of justification, the constitution of the Church, the primacy of jurisdiction of the Roman Pontiff, and the only true union by the return of the dissidents to the one true Church of Christ. It should be made clear to them that, in returning to the Church, they will lose nothing of that good which by the grace of God has hitherto been implanted in them, but that it will rather be supplemented and completed by their return. However, one should not speak of this in such a way that they will imagine that in returning to the Church they are bringing to it something substantial which it has hitherto lacked. It will be necessary to say these things clearly and openly, first because it is the truth that they themselves are seeking, and moreover because outside the truth no true union can ever be attained.

III—With regard especially to <mixed assemblies and conferences of Catholics with non-Catholics>, which in recent times have begun to be held in many places to promote "union" in the faith, there is need of quite peculiar vigilance and control on the part of Ordinaries. For if on the one hand these meetings afford the desired opportunity to spread among non-Catholics the knowledge of Catholic doctrine, which is generally not sufficiently known to them, yet on the other hand they easily involve no slight danger of indifferentism for Catholics. In cases where there seems to be some hope of good results, the Ordinary shall see that the thing is properly managed, designating for these meetings priests who are as well qualified as possible to explain and defend Catholic doctrine properly and appropriately. The faithful, however, should not attend these meetings unless they have obtained special permission from Ecclesiastical Authority, and this shall be given only to those who are known to be well instructed and strong in their faith. Where there is no apparent hope of good results, or where the affair involves special dangers on other grounds, the faithful are to be prudently kept away from the meetings, and the meetings themselves are soon to be ended or gradually suppressed. As experience teaches that larger meetings of this sort usually bear little fruit and involve greater danger, these should be permitted only after very careful consideration."

Be aware that an Eastern Orthodox is validly baptized. The only thing they have to do to be a Catholic is to reject their errors and they are Catholic the next minute if they did a perfect act of contrition, not so easy, so it is not a certain, so they would have to go to confession for a certain, if they are truly repentant. That's it.

She is not at this point, yet.

As far as being accepted formally by an SSPX priest others can tell you the procedure.

As soon as my wife asked me, I called my priest and he was absolutely ok for her to come with me to the Mass and only asked that she wait in a side room, after the offertory. But before the Mass he was very jovial, welcoming and cordial to the point that he invited her to sit right at the front, on the very first bench. My wife preferred not to, and sat at the back. The homily was about else but, at the end, he touched on the prodigal son parable. After the Mass he instructed a young parishoner to run to fetch some cake and fruit juice. We are very, very small congregation of about 20, and there was no mention of converting anyone or any talk of religion, we simply ate and and chatted amiably. Everyone made her feel very welcome. Hence my tears of joy...

People often say, “It is better to be a good Protestant than a bad Catholic.” That is not true!

I never said that this is my conviction. Only that this is what I was told and wanted to believe.

That is correct.

Can you please explain more about this obligation? I am not aware of it and its impications.

I can understand how it was wrong for them to ask of me this but, how did I do wrong to concede to make that promise?

Am I not free to omit a an action that is not mandated?

I understand that I am not free to, for example, omit going to church on Sundays. But am I not free to omit charity to a vagrant in a street?

The whole thing was wrong because for the very same reason that the Orthodox granted you a dispensation, it is quite probable that the Catholic Church would not have - imo. Put it this way: if you were to tell a Catholic priest you will marry her on the condition that you promise to not even pray for her conversion, do you think the priest would give his ok on that?
You're supposed to prod your spouse, *however so gently and slowly that may be*, toward the true faith, at least by your example so that she gets sanctified in seeing you live the true faith.
 
  

The whole thing was wrong because for the very same reason that the Orthodox granted you a dispensation, it is quite probable that the Catholic Church would not have - imo. Put it this way: if you were to tell a Catholic priest you will marry her on the condition that you promise to not even pray for her conversion, do you think the priest would give his ok on that?
You're supposed to prod your spouse, *however so gently and slowly that may be*, toward the true faith, at least by your example so that she gets sanctified in seeing you live the true faith.

Marriage between Catholic and Orthodox is canonic in the Catholic Church but not in the Orthodox, or so I imagine, given the hurdles we had to overcome.