For me it is myself and my in-laws who don't get along. So the situation isn't exactly the same. I realize that you aren't in that relationship anymore, but for the future here's my advice.
I elect to be civil, if a bit distant. I won't start an argument, and if one erupts, out of respect for my wife, I prefer to merely leave. She may choose to stay and spend time with her parents if she wishes. I understand that she needs time with them. I won't hold it against her at all. Nor do I particularly want her to side with me all the time. Only if they get really out of line do I expect her to do anything.
From your point of view, you should try not to take sides, as both are important to you, and if your SO or parents expect you to choose then tell them off. Expecting you to choose sides is an outrageous expectation, under the circumstances. Ultimately, if your parents can't behave, then see them less and less, until they get the point, or they are out of your life. You don't need the stress and it is YOUR life, not theirs. If your SO is the problem, then you will need to have a talk with her and let her know that she is putting you in a tough position that you'd rather not be in. If she demands that you back her up, then frankly, you need to find someone else. She ought to be able to handle her own arguments and ought to be aware enough of your feelings to not put you in that position. If she is incapable of that, then she isn't good GF material.