Regardless of the fact that her family was on your side during the breakup with your ex. Lets use some common sense here, how on earth do you think a relationship with your SIL is ever going to work?
Aren't there any other girls out there besides your SIL?
Have you forgotten the fact that they are sisters and they always would be. Is not like they are just friends or best friends. The only person who is going to get hurt in this awkward relationship is You.