Girlfriends family

My girlfriend (25F) and I (29M) have been dating for three years. I was not raised in a home that embodied the “family” aspect most people think of so marrying someone who had strong family life is important to me and something I always looked forward to because it felt like I had missed out on it. My girlfriend knows this.

A few months ago my girlfriend texted me screenshots of a texts from her only sibling, and twin sister saying how much she didn’t like me going into detail of how my girlfriend had previously said “it’s not like I’m going to get any better” (she denies saying this). She continues on in the texts about how I’ve never made any attempt to get to know any of their family and how she doesn’t want me to be apart of it. This came as a major shock and part of me wishes I hadn’t been shown the texts, but on the other hand I’m glad I know. I’ve always been respectful and made every effort possible to get to know each of them. I’ve gone out of my way to celebrate them on birthdays and holidays. I’ve been faithful, respectful, and loving to her sister and am not sure what else she wants from me. I’ve brought this up numerous times to my girlfriend and expressed how important family is to me and I’m scared if I propose I’ll be walking on egg shells the rest of my life around her family. I’ll bring it up, we’ll discuss it, she’ll assure me time will fix it or that she will sit down with her family, but it all just kinda gets lost in time. Her sister lives with her parents so I worry she has alienated them, as well.