Having a partner who's got another partner can be a lot like having a mother-in-law (especially if you're a woman). You both love the man, but are you going to end up united by that love, or rivals for his respect and attention? Are there pissing contests over who's in charge, who's got more authority, who does he love more, or are both of you secure in that he loves you both (equally?), or is the hierarchy clearly defined and everyone's at least OK with it, is there a hierarchy and does the one who hasn't got the authority keep lashing out at the other?
It's not something that's determined so much by the position of having a mother-in-law or not that determines how things are going to go between the two of you -- obviously, if his mom's dead, or if he doesn't get married, he'll never have the dynamics between wife and mother to worry about, he'll just have the one. But if he does get married and his mother's alive and in any sort of contact with him, his mother and his wife are necessarily going to have some sort of relationship with each other, just by virtue of both existing in the same namespace.
If one of the women is a controlling bitch who says she must love and obey her first and only, and he's got another deep relationship, shit is going to go down. If both of them are that way, even more so. If both of them are easygoing and okay with the other, it's all going to be good, unless he does something completely funky and both of them get pissed at him.
I actually like this model more than the siblings/parent model, because it's more expected that siblings should get along and/or love each other, no matter if they actually do or not. It's natural to have family bonds with people you scrap with from time to time. Whereas, if you've both paired up with the same man, and aren't involved with each other, there can be tensions. The mother-in-law/daughter-in-law relationship is more equal than the wife/mistress relationship, and there's less of a clear outline on who has the power by right. Things often fall in favor of the wife, but then if there should be a divorce... and then some people do favor their blood family over their married family, and go with the blood family decisions and overshadow their wife's say in things...
Expecting two girlfriends to get along is like expecting your mother and your wife to get along. Maybe they will, maybe they won't. You can help the process along, but it's only going to work if they both want to and both can get along with the other...
I wanted to get along with BJ's mother. Well, sort of. Truth be told, I hated her and would have wanted her to die except that this would have left me as clan mother, and I couldn't stand most of the clan. But I didn't want to fight with her. I just wanted to crush her utterly and never see her ever. It wasn't that I was opposed to my fiance having a mother, it was just that the one that he had was an unreasonable psychotic bitch, and she and I couldn't stand each other even though we pretended to be polite. That somewhat compared to when my ex the redhead was boinking his friend V. I didn't want to fight with her, I just thought she was a psychotic bitch and bad for him, and would not accept anything other than him not sleeping with her.
And then there was good ol' Shawn's mother. She is a sweetheart, a wonderful woman, and damn near a saint. She and I loved each other on first sight, and got along excellently, much to Shawn's dismay. I would take her as a mother-in-law any day, if only that didn't mean that I'd have to marry Shawn. My ex the redhead sort of had a girlfriend like that -- the girl after he moved out of here was nice, interesting, and I got along with her well -- he was surprised to hear that I was just fine with the idea of him getting it on with her, and very happy about it, even! He'd thought that actually I wasn't really poly, I was just using it as an excuse to sleep around, so my actually approving of him getting it on with another girl was very much a shock to him.
It's not that the relationship structure is inherently flawed, so much as it is the pre-existing personality flaws, strengths, and quirks of the participants, and how they choose to arrange the rules.