AITA for refusing to babysit my half-siblings and telling my dad I’m not his “backup mom”?

Hi Reddit, I (19F) think I might have gone too far, but I need some outside perspective.

For context, my parents divorced when I was 12 because my dad cheated on my mom with a younger woman, Emily (now 31F). It was a messy, ugly divorce, and my relationship with my dad has been strained ever since. He married Emily pretty quickly, and they now have three kids under 5. Ever since the kids were born, he’s been constantly asking me to “help out” with babysitting.

I live with my mom and go to college full-time while working part-time to cover my expenses. Despite that, my dad calls me almost every week, begging me to come over and “bond with my siblings” by babysitting. He says Emily is overwhelmed and needs a break. I honestly don’t care—I never wanted siblings, and I’m still not over the fact that his affair blew up our family. I’ve told him I’m busy with school and work, but he keeps guilt-tripping me, saying things like, “Family takes care of family.”

Last weekend, he called again, practically demanding I babysit because Emily had a “mental breakdown.” I lost it. I told him, “I’m not your backup mom. You chose to have more kids, and that’s not my responsibility.” He got quiet and then said, “I thought you were more mature than this,” before hanging up on me.

Now, both he and Emily have been sending me messages, calling me selfish and saying that I’m abandoning my family. My grandma even chimed in, saying I should “help my father in his time of need.” But I feel like he’s just trying to dump his problems on me because he made bad choices.

My mom thinks I did the right thing, but now half my family is pissed at me. AITA for refusing to help and saying what I did?