I have a non sexual boyfriend. We have all talked about it, all of us in his and my life, and have come to terms with the fact that we love each other, but our relationship is not going to go in that direction. It might be strange to mainstream culture, but we here in polyland
make our own rules. As long as everyone is being respected, being honest and open, communicating, keeping each other in mind and keeping their integrity then really the world is your oyster.
I would suggest thinking about what you want from this. How can you benefit? How can she and he benefit? Then talk to them both. If you are that uncomfortable then maybe its not for you. That's okay, but it might be a good idea to tell her that. It sounds like she is taking it personally and hurting. Some reassurance that you care about her but don't want to go down the route of being her part time husband, or whatever it is she thinks you are, could go along way.
If it is something you could handle and benefit from, then it might just be time to talk about boundaries. What are you okay with? What are they okay with? Maybe you don't like what she calls you, but are okay with other things. A good long think is a good place to start I think. Do some reading here too.