A.B.
I would say trust your instincts. If it feels out of control to you, then you need to do something about it for your own peace of mind. A parenting class is always a good idea. There are also a number of good books you can take a look at. One that comes to mind is Siblings Without Rivalry (Faber/Mazlish). Since both you and your boyfriend work full time, have you spoken with whoever takes care of the children during the day about their behavior? Is it worse or better when you're not around? I'm also curious why your relationship with your son's father has been hard on your daughter? If that's true, then she could be acting out based on some emotional hurt/struggle she's having.
It sounds like there could be a number of things going on. You might want to think about some family counseling too. A professional watching how you interact with your children might be able to give you some good insight into anything you're doing unconsciously to contribute to them not getting along - and help reinforce what you're doing that is already good/helpful. Just a thought. Good luck