Love my partner, can't deal with her kids...

I am divorced with an 8 yr old daughter who lives in a different country. I have been seeing a wonderful woman for a year now. She is also divorced and has two young boys (4 and 6). The boys' father is still very present, and the boys see him and their mom (my partner) in a 50/50 sort of timeshare arrangement. I have met the boys' dad, and we get on fine. The time I spend with my partner one on one is great. She's kind, caring, fun, smart... But her kids are turbulent and I really don't like being around when they are there, because the whole dynamic between her and me changes. Without exception, every time I am present when the boys are there, there is a tantrum of some kind from one or both of them. Unless my presence causes it, then it must be pretty much constant. It does my head in. I am not the boys' father, and cannot step into that role. Their behaviour frequently makes me very tense, and my parenting style is very different to that of their mother, and probably their father too (although I have never seen them just with their dad, so I don't know. If I were to try to step into that role, it would be confusing and confronting for the boys, as I would be much stricter with them than their parents are. But it will never happen. I'm not their dad. I don't want to break it off with my partner, and I'm sure she doesn't either. She is aware of my reticence to be around the kids, and doesn't really know how to deal with it. It's a difficult topic, because she is obviously torn between her feelings for me and her feelings for her own children. It's a horrible contradiction and I don't want to be putting her in that kind of position, but I can't "pretend" to get along with two boys whose behaviour frequently makes me extremely uncomfortable. I don't know what to do. Obviously we need to talk about it, and we have tried in the past but I think we are both avoiding the subject a little - hoping it will "work itself out", despite how dumb we both know that is - because neither of us want her children to put and end to the wonderful relationship that is developing between us. I'm not expecting miracle solutions, but maybe someone out there has been in a similar situation and has some wise words? Thanks.

Thank you ALSOSUSAN2... You are right, ultimately my partner's relationship with her kids outweighs everything else. Thanks for the perspective.