Fuck apologizing to the parents. Apologies are for when you've done something wrong, LW has done NOTHING WRONG, certainly nothing wrong TO HER PARENTS (maybe she did a wrong thing by cheating on her boyfriend, but maybe they were broken up at the time, or had agree to an open relationship, or something).

On the other hand maybe she wants to make nice with her parents, maybe they will give her money, money is nice. But the strings that come with the money may be too much to bear, LW should think carefully about what she is prepared to put up with before pouncing on the possible money.