We send them as a family, and they do send texts, cards and presents to my partner so I don’t think I am being a “passive mug” for counting myself as a family with partner and including my name.
You are a family with your partner, absolutely. But they're not treating you like family, unfortunately. They take your cards and presents year after year but send you nothing back unless forced by your partner. When you keep sending cards and presents, they think you're happy taking the treatment they're dishing out.
Especially to the nieces and nephews. Would it not be excluding myself more if I just removed my name from everything as if I didn’t exist?
No, you'd be simply letting your partner do the sending. He can include your name if he wants to.
He is totally capable of it, and did it when he was single, but I enjoy it, I like picking cards, wrapping presents, writing the cards and posting them. He gives me the money for the cards, gifts and postage. I never said he wasn’t capable.
But he's not capable of standing up for his partner and asking them why they exclude you? Instead he is passive with them and tells you that he doesn't understand why you are upset. Maybe miss his birthday one year and let him see how it feels to be left out?
Does he open his cards and presents from his family in front of you?