I wish I had more information. You are now 18. You say you dated this guy for two years when you were younger. That means that maybe you were 14 or 15 or so, maybe even younger. What you described as “cheating” may have been his awkward effort to separate from a relationship that was too serious too early.
It’s normal for teens to try on different relationships. It’s a time of life when we figure out what kind of person we want to be with and how to be in a relationship. Kids often don’t know how to end a relationship gracefully so do something stupid or thoughtless in an unconscious effort to gain the freedom to do more exploring. It’s hurtful but it isn’t necessarily an indication of the quality of the person when he or she matures.
You are probably right that your parents are only trying to protect you. They saw how much you were hurt. They may not share the perspective I outlined above. They may also have information I just can’t deduce from a short letter.
I also don’t know how you and your parents are are talking to each other about the situation. If you are angrily insisting on your right to love who you want to love, you aren’t showing them the maturity you claim to have. Telling you not to tell him about it if you sneak may have been your father’s best attempt to grant you some privacy while at the same time avoiding dealing with a situation that is painful for him. Anger and avoidance aren’t helpful when trying to solve a problem.
You are a young adult still living in your parents’ home. It is not at all uncommon for there to be relationship struggles between parents and their kids who are emerging as adults at this stage of life. Most families go through a period of uncertainty and tension around boundaries, privacy, and whose rules are “the” rules. Getting through it together helps the family as a whole transition out of child rearing to adult-to-adult relationships.
There is no need to “ruin” your relationship with your parents in order to have the freedom to explore whether this relationship really does have potential. The three of you do need to find new ways to deal with each other when there are important disagreements. This one won’t be the last one, I assure you.
For that reason, I urge you all to consider seeing a family counselor for a few sessions for some guidance and support. I’m not suggesting that anyone is deficient or “wrong”. I am suggesting that it is important for all of you to find new ways to manage solving problems with each other. If you could do that, you would have done so already. Now is the time to learn some new skills that will set in motion a healthier style for settling disagreements with each other.
I wish you well.