It depends. Even with Ursa around, Ozai would have been there too, and she was obviously always much more likely to listen to and follow her father than her mother. I can't see Ursa ever completely giving up on Azula, but if she had been able to stick around, their relationship probably would have just gotten more and more strained and Azula would have grown even less and less likely to listen to anything she had to say. Sadly, with Ozai's influence as strong as it was, I don't think Ursa's presence would have positively affected her much.