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Question is:

does the term laver of regeneration mean the sacrament itself (with desire included in that term, because without such desire no sacrament is effected)  ?

That's precisely my point, you think the sacrament alone suffices for justification.

Laver of regeneration alone =  no desire

The reception of the Sacrament alone does suffice for justification. But the Sacrament cannot be validly received if the recipient is forced to receive it. In the Catechism of Trent, in the Sacrament of Baptism chapter, Section "Dispositions for Baptism," it states,

"The faithful are to be instructed in the necessary dispositions for Baptism. In the first place, they must desire and intend to receive it; for as in Baptism we all die to sin and resolve to new life, it is fit that it be administered to those only who receive it of their own free will and accord: it is to be forced on none."

So the "desire" in the phrase ["without the bath of regeneration or the desire for it"] is the "desire for the Sacrament" (as in a catechumen's desire). At root, it is a recognition of one's sinfulness and a desire to be cleansed of that sin. The Sacrament is the normal instrument of that cleansing. 

The "desire" referred to in Trent is not some generalized "desire to go to Heaven." Yes, justification assumes that generalized desire to be saved. But that generalized desire is not sufficient. It must be joined with an act of the will which DECIDES to receive the Sacrament of Baptism because the catechumen recognizes that he must be cleansed of sin before he can go to Heaven, which requires the Preparation discussed earlier.

The Anti-BoDers fail to understand the proper understanding of BoD, and assume that all supporters of BoD are Rahnerian Universal Salvation lunatics. That is not what Tridentine BoD, properly understood, is referring to. The Anti-BoDers throw out the baby with the bath water. And in doing so, they teach heresy.

As described in that paragraph, one is "translated" from the "state of sin" into a "state of grace" (which translation ends in what is called "justification") by either receiving the Sacrament of Baptism OR the "desire to receive the Sacrament of Baptism." Exactly what God does with the justified soul, which through no fault of his own cannot receive the Sacrament he desires and has made a decision to seek, is not discussed in the Trent decrees. Trent just says that he is "justified."

and desire on the part of the recipient is implicit in the reception of the Sacrament because the Sacrament would be invalidly received if forced

I'm trying to find a source to confirm that it would be invalid, rather than merely illicit.

In other words, if the character of Baptism is still received, despite being forced, that would be valid, but illicit.

If a forced baptism is invalid, then there is no other way of reading the text, and no sacrament is conferred. Thus, the term laver of refrigeration could not mean anything other than the Sacrament of Baptism with the desire included implicitly in that term.