I think you should try to get the idea out there that you are not property and, therefore, you can not be stolen. Neither one of them has the power to make you care for the other less. Then try to find out why she is feeling that way. It is not easy getting people to talk about these feelings, but if you can get it started, it pays off long term.
As for the mother, she will accept it or not. Her main focus will probably be on the happiness of her daughters. If they accept the relationship, then she may evebtually accept it.