My family excludes my girlfriend and that upsets her

To give some context, my girlfriend (27f) and I (28m) have been together for a little more than a year. We see each other 4-5 times a week. I currently still live with my parents to save money but I hope to move out soon. My twin sister is living out of town and visits about once a month, and she doesn't like my gf all that much because she thinks that my gf is taking too much of my time and preventing me from spending time with my sister.

My family likes to plan things with me like going to dinner or watching a movie or what ever the case may be as a family, and when I tell my girlfriend that she feels left out. I stick up for her when my family wants to do something and I want to invite her but they don't want her to be there, they just want me.

My gf doesn't want to be treated as an option on when she can or can't participate in things with my family. I've tried talking with my parents to be more inclusive but their argument is that they just want to be together as a family and that it's nothing personal, but they feel that she is invading our family as they think that she always wants to be involved.

We've had this problem for a long time now and I don't know what to make of it or how to fix it. Because I love my family and I want to spend time with them but I feel that they aren't as accepting of my gf, and I also don't want to ditch the family plans as well to spend time with my gf bc I also want to spend time with my family. Where do I go from here to make all the parties happy?

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TD;LR - my family wants to spend time with only me, and my gf feels left out