I just don't see how anyone wins if you have to choose. You will resent having to choose and question if you made the right choice, while the lady you do choose will wonder if you wish you had chosen differently. Not being willing to solve the issues between themselves, could be an indication of your future with either or both of them. What happens when you become the focus of their wrath, will they be willing to find a solution?
Is it that they don't want to share at all or just with each other?