YTA. If she had tried to say you couldn’t go see your friends once a month, she would be the AH. But she is asking to for you to not see them this once, for her mom’s birthday - which comes once a year. Her mom has planned this event, and it would be offensive to ask to change it so you can just hang with your friends. Then your “gotcha” test was rude and manipulative. You act like you caught your gf in some contradiction - but you didn’t. She said her mother would not celebrate her birthday on Sunday cause it was “the lord’s day.” Now you (or I) may not agree with that, but clearly religion is very important to your gf. So her not being willing to miss church for your sister is consistent with this position - and as she said, your sister is welcome to join you. You are valuing your hang out day with your friends over good relations with your gf’s mom. Which bodes poorly for the future of your relationship. What if your gf gets pregnant and ends up going into labor on that day? What if your gf falls down and breaks her leg on that day? Your relationship and family should come before your hang-out with your friends.