This is a very tricky situation. I think it truly comes down to you looking inside yourself, and deciding if you're comfortable being a secret to her family. I understand for her it's too difficult to tell her family about you, and from what you said she will never, ever budge from that POV.
Are you ok with this? is it something that will build resentment in the future? i know these are difficult questions to think about, (and i'm sure there are more) but i think it's important to find the answers.
While you definitely care about her, you still need to pay attention to your needs.
I'm in a similar situation as my gf feels like she can't tel her family about our poly-ness, while i tell my family everything, so i do feel for you. (but this isn't about me)