Your mother is being rude in this situation. She is in the wrong, and you shouldn’t push her unreasonable agenda here. Explain to her that it’s not polite to ask for an invitation to someone’s birthday party. Your boyfriend’s family may do things differently than yours, and that’s their prerogative. His mom can choose who to invite to things. You’re not going to push for an invitation any more than you already have. You’ll make plans to have them over another weekend.