So me and my gf have been together for over 4 years at this point, we were long distance for a long time and recently moved in together. She left her home and moved over 22 hours away and she has been having issues. She's been okay for the most part but recently it was Father's day and she had a pretty hard time but this isn't what this post is about.
She suffers from fairly bad anxiety and often overthinks things. She also claims that she has always had problems making friends possibly because she just overthinks and thinks nobody likes her but I don’t think it’s entirely true because of course I’m biased but she is incredibly kind and super thoughtful but she does speak her mind and isn’t afraid of telling things how they are. Ever since she moved here it has been very difficult to convince her that my parents like her even though to me it seems very apparent that they like her and see her as a part of the family. A little more backstory of the situation, she moved here in September, and we live at my mom's but visit my dad's once a week and usually have dinner. In December my sister had a friend stay over once and then he proceeded to stay, he isn't dating my sister (he is gay) and my dad and my step mom have brought him into the family.
Fast forward to this week and they had a birthday party for him and we went over and celebrated. During that visit, my girlfriend, my dad and I had a really long deep conversation on the porch while it was raining. I thought all was well but she told me tonight it bothered her that they threw a whole party, small mind you, for him but they didn't wish my girlfriend happy birthday on her birthday back in november and they forgot and told her happy birthday on the usual day we come over. I have told her that she is overthinking and she brings up some good points but I do know that my dad and my step mom like her but she feels like they see my sisters friend more a part of the family than her and I keep reassuring her but she seems stuck in her beliefs. They did get her a Christmas gift and even got us Easter baskets and I genuinely believe they like her but she won't believe me. My dad even said that he understood her feeling on Father's Day and said he hoped she feels better knowing that she now has more family here but she still doesn't feel like they see her as family.
I know it's a tough situation but I would just like some advice on if I'm wrong and she could be correct or if she really is overthinking about them forgetting to wish her happy birthday as this sign they actually don't see her as family. Is she overthinking it or am I being too forgiving of my family?
TL;DR My GF keeps overthinking about how she thinks my parents don’t see her as family and I am trying to convince her that my parents actually like her.