She told you if she can't be on his team then she will quit the sport. That is what she should do then if she's unwilling to adapt to the compromise that you suggested. Don't feel guilty that's she's quitting something she loves doing. She is cutting off her own nose to spite her face. She is expecting that you'll say "Oh don't quit I know how much you love it." Well, don't give her that satisfaction. A deal is a deal. Remind her of that and if she breaks up with you to do the sport with lover boy, then you know how much you were actuall valued (or not) early on and you can leave before she cheats on you with him a yet again.
Are you sure you two really want to be together?
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion