ShouldI I end the relationship

If she is brainwashed by her mom, it will be very difficult to make her believe your opinions and make her like you. Even the dad will have difficulty doing so, especially if she is the one who lives with the daughters and he is only seeing them a few days a week. Even if the daughters live with you, I see how the ex-wife can influence them against you, as you are an outsider and they would choose mom over a stranger any time of the day. And the idea of their parents getting back together is most probably more appealing to them than to live with a stranger.

People always fear change and this case is no different. And to make things complicated, it involves teenagers, who already are rebellious to anything around them at those ages and you seem to be caught in a cross fire.

The first thing you can do to make you feel better is to accept that they will hate you for the rest of your life and embrace the fact that you are an outsider just happened to be at the right place at the wrong time. By saying that you should accept it, I don't mean you should stop trying to be nice to them and change their minds about you. Just do it with moderation and don't expect anything in the short term, because if you do expect a quick return, the only thing that will happen is that you will get disappointed over and over and get discouraged to work on it, which then will eventually take its toll on your relationship.

You have a slight edge over here too. Teenagers go thru a sleuth of emotional outbreaks and are always judged by their parents and then grounded for their actions and a whole lot of other drama. This is clearly one of the times where they would need advice on anything and everything, but without being judged. You can use this to your advantage, where you can be the goto person when the daughters feels like they need to talk to someone and get advice without being judged and getting reprimanded.

While doing so, you don't want to say or do things to conflict the mother, which will only anger her more and make her more vicious in her actions to get the daughters to hate you. But you can approach them as a friend who needs you the most when going thru a bad time and give them the kind of advice that will only make them a better person. And at times, if you feel that you are advising the same thing as the mother does, praise her and try to make the daughters understand why she would say such a thing. That will clearly let them know that you are not an outsider or a total stranger, but someone who happened to fall in love with their dad.

I think I went off the tangent a bit but oh well... good luck...

If you think, your boyfriend may actually get back together with his ex wife, I think you should end it. If you don't, his daughter would have all the right in the world to blame you, now and forever.
But if you are positive and certain that they will not get back together, you should ask for your boyfriends help, to make his daughter believe that it will not work with her mom , regardless if you are in the picture or not. She will not believe you, so you definitely need your boyfriends help. After she is convinced that you are not reason they broke up, you may have a chance with her but not until she knows it's not because of you. And in my opinion, as I said, you can not do it by yourself.

I agree with both these guys 100%. The only thing I'd add is that, as you probably remember, teenage girls barely like their parents, let alone their dad's girlfriend and 15 is the heart of the toughest years. Your boyfriend needs to help fix this for sure and you need to keep in mind that all relationships will have challenges but someday, those girls will understand the truth and you will move past it.