Short background. I've been married for almost 15 years. My wife and I are currently separated and I am going to meet with a lawyer soon about divorce. My wife initially left me, moved in with her mother, and took my two children with her. After about a month, for the kids sake, she moved back in the house, but had her own room she treats as an apartment. We interact as coparents and friends and that is all. I'm happy with this arrangement.

This background is relevant because an acquaintance that I've known for 4 years and I have recently started seeing each other. It's an awkward situation for me because she has requested that I don't have sex with my wife and only have sex with her (which I am perfectly fine with) and that for the foreseeable future I'm the only person she is going to have sex with, but she doesn't want to be called my girlfriend and doesn't want to be exclusive. Last night, she gave me a key to her house, bought me a toothbrush and shampoo to keep at her house, asked me to bring clothes here, and offered to let me move in with her rent free. She told me she loved me, that she thinks that she'd be a great step-mom to my daughters, and even bought them a gift. She even offered to pay for a hotel for my birthday to take a beach trip with her and my daughters. She told me that we could make a great home together, that I'm starting my life over again, and that she doesn't want me to ever have to start over again. There's still no labels and she doesn't want anyone to know. She said that she'd be more comfortable after I meet with the lawyer.

So, here's my question, am I basically in a relationship (that appears to be long term) and she's not wanting to put labels on it or be open about it because I'm not divorced yet?