My 10 year old daughter has temper troubles and behaves very rudely with my girlfriend. how do I find out what’s wrong?

i think it is natural for her to be rude and behave like this towards her, as she will be feeling insecure. but this is mainly because she loves you and may be worried about how all this means for the relationship that you and she share. also, start spending more time with her and talk to her about it when she is not too angry. maybe a change of scene may help so take her out on a small weekend trip and let her enjoy, and don't make it seem as if you took her out there only to talk about your relationship. give it time. and understand her too.