This is not only your problem it is a general problem in every house due to the western culture we are adopting. Girls, specifically during their young age just see the benefits of nuclear families which they have seen either in their parental house or friends home. They never understand the benefits of joint family because either they have not lived in such family or have not seen such families.
Is the family of your bhabhi a nuclear one? It seems that your bhabhi came from a nuclear family and in that case you can seek the help of her parental family to make her understand. But as mentioned by you, you might have tried that also.
According to my experience their are some unwarranted issues between your mother and bhabhi. Ego, attitude or habits may be a cause. Such issues are not so big but they could not be resolved because of ego or non-cooperation. Both your bhabhi and mother need to sit together and clearly speak out the issues which create unnecessary arguments. But for this sitting with open mind and without grudges is a must.
Some one of your family who enjoy good rapport with both can mediate to ask the issues they have with each other because according to your post your bhabhi has issues with your mother only. You can also ask your mother to talk to bhabhi’s mother directly and tell her the issues but in that case your motheris also required to understand the problems of your bhabhi.
If you expect any easy answer to this problem, it is not possible. Both your mother and bhabhi must understand that the family is incomplete without the other.