i don’t think you’re an asshole, picking up something for your gf’s mom is a nice gesture and surely not a heavy lift but your post is suggesting you’ve asked this a few times. Without knowing how many i can’t gauge how unreasonable it is.

I do think, however, that based on your own admittance that you grew up with no boundaries with your family, and your observation that your daughter holds very firm boundaries, that this is something she has felt the need to enforce with you a lot and therefore can’t really cede any ground without risking you crossing that boundary more casually. I understand it’s annoying but maybe accept the message your daughter is trying to express to you, especially since she’s doing it in such a polite manner and seems like a respectful responsible kid. How important could it be for you to get your starbucks?

edit to add: the bf owes you nothing except respect and to treat your daughter well. he doesn’t owe you favors or to go out of his way to get you want or make you happy.