AITA for refusing to let my ex’s stepchildren join my kids and I for some family traditions?

My ex (33f) and I (33m) share three children. Alannah (10), Jonah (8) and Callum (7). My ex cheated on me two years ago and left to be with her affair partner who is now her husband. She and I share custody of our children (50/50 timeshare) while they have full custody of her husband’s two children from his previous marriage, that ended with the affair as well.

I was always an active dad in our kids lives and we had our own little traditions from baking brownies the day before they go back to school and having a little brownie party, to baking cookies for their birthdays and letting the birthday kid pick what kind we make, to doing a group photo for Halloween every year with our costumes and doing silly faces and our Christmas shopping day where I take the kids and we make a day out of buying the gifts. We go out to eat, get photos taken, sing Christmas songs in the car, etc. They might not be the most traditional traditions around but I have done this for years with the kids.

My ex asked our kids if we still did those things recently and they said yes. She then told me I should include her stepkids in these sometimes because our three are bonding during these experiences and are coming together as a group that doesn’t include their stepsiblings and since her stepkids are not going to know our kids as stepsiblings but will only know them as siblings, because of the age and the fact they are always with my ex and their dad, it would be cruel to let them be frozen out like that when I could help the bond.

I told my ex I did not want to include her stepkids. I said she could come up with traditions for them to do as a family unit if she wants. But I am not going to be more involved with her cheating ass or her affair partner than I need to be. I told her being civil for the kids is the best we can ever be and there is no way I want to take responsibility or bond with her stepkids. She called me an ass and said I am putting my feelings before those of two young kids. She said it won’t bother our kids at all because they’ll always see the stepkids as interlopers but two little kids will always feel othered and it will be my fault because I’m a dick. She also accused me of being gleeful about the pain of kids. This is not true at all but she thinks that my having this boundary is me rubbing my hands together like a cartoon villain.

AITA?