Lets say that you are sitting around thinking about an injustice that has been done to you, and your natural reaction causes you to become angry and start dealing with thoughts of revenge. Note how I said "natural reaction". So fi this desire was natural would it be a mortal sin? Or would you have to realize, at some point, that this desire is mortally sinful then continue to dwell on the desire, unchecked, for it to be mortally sinful?
It is analogous to the sin of lust. If an intrusive carnal thought enters the mind, that is not in and of itself sinful, and as long as you resist the thought, you commit no sin.
Entertaining carnal thoughts, however, is the sin of lust, just as entertaining thoughts of vengeance is the sin of wrath. Our Lord makes the analogy as well: saying that entertaining angry thoughts about one's brother is killing him in one's heart, just as entertaining lustful thoughts is committing adultery in one's heart.
Emotion is not without its place. Its proper place in man is as a motivator to action, but we must guard ourselves that our emotions impel us toward good and holy actions, not sinful ones.
I suppose that my question has everything to do with "entertaining" things. So if you are angry about something then start thinking about physically harming someone else it is always mortal sin?
Reason I am asking is because I find myself in this situation, but then eventually I realize I need to stop. Then I stop. It seems I am not entertaining it because eventually I realize what I am doing then I make an effort to stop. My concern is that I may have committed mortal sin since it is one of those things that can be mortally sinful. It seems to me that it would become mortal sin at the point where I realize it is a grave matter and then I keep entertaining it after that point. Am I right?
While I'm not entirely sure that what you describe is common among Traditional Catholic men, it wouldn't surprise me at all if it were; for I myself have struggled frequently with this very same temptation.
We are, by our nature and God's will, the dominant and more aggressive sex. Add to that the fact that we, as Traditional Catholics, are living in a perpetual state of self-defense; against sin, against the world, against temptation, against wicked people, and, for the past 40 or more years, against the heretical influence of the vast majority of what is at least outwardly, and apparently, the heirarchy of the Catholic Church (something utterly unprecedented in history). With this being the case, and with our society growing more and more tolerant of error and sin and evil, and more and more hateful of God and His Law, it is no wonder that Traditional Catholic men would have short fuses.
I travel far from home to take my family to Mass on Sunday, and yet there is a beautiful old Catholic Church only one block from my house. If I were born a century earlier, I could simply take my family to that Church or to any Catholic Church anywhere on earth, secure in the knowlege that I would see the same thing anywhere I went - the holy Sacrifice of the Mass, beautiful and reverent and the same everywhere. But if I step into that Church today, I would see women traipsing in the Sanctuary, reading from the epistle and distributing Holy Communion, a polyester-wearing priest facing the people, and service that far more closely resembles a Lutheran gathering than the Mass of Ages... and this same sad fact holds true for most Catholic Churches in the world today. That one lamentable fact alone is a frequent cause of grief and rage for me. No doubt that anger is righteous in its beginning, but it ceases to be when I let it fester within me and entertain the vengeful thoughts it engenders.
Also, I live in New York City. So I see things that enrage me literally every single day. So believe me, I know what you mean when you describe the persistent anger that wells up within, and the desire to take action. But even just anger can impel us to bad thoughts and actions. And we must always remember our place in the world and chastise our flesh with prayer and fasting. Also, take heart that no Injustice escapes God's eye: "Revenge is mine, I will repay, saith the Lord."
And yes, you are correct that, as long as you do not wilfully, intentionally entertain the thought it is not sinful. Though you may be plagued by such thoughts all the day, as long as you fight it when you become aware of it, you commit no sin. If anything, you will have something to offer up as penance.