AITAH for refusing to let my son take his Christmas gifts to my ex-wife’s house to “share” with the other children there?

My ex-wife and I had a bitter divorce 6 years ago. We don’t get along and we don’t communicate about anything other than our 10 year old son and when it comes to him we often disagree on big decisions and we need mediation to come to an agreement and at times that also means we end up in court for a decision.
Things have been worse on that front since she remarried. Her husband has three of his own kids (18+, 9 and 😎. They also have a 4 year old together. The problem since her second marriage is the belief they have that I have a duty to make sure things are fair and equal between the children in their house AND because they have a belief that their household is more important and that certain experiences belong to them as a family and that I should refrain from doing those things with my son.
Examples of this are when I took my son to Disney and they were upset because they had a five year plan to take their family there. This was never mentioned to me and I felt it was unfair to say I couldn’t bring our son until they got to take him. Another example was signing my son up for ice skating lessons when he wanted. I signed him up close to where we live, which my ex signed off on at first, but then they couldn’t afford it for the other kids/couldn’t give them similar opportunities and it was a big deal. We also had issues with my son’s birthday parties when I throw them because they can’t compete with what I do (take my son and his chosen guests somewhere cool) and their other kids don’t get the same. Added to that was the other kids not being invited but my son didn’t want them there and I let him decide the guest list.
My son loves gaming so I got him a console for Christmas. My ex saw me buy it a few weeks ago and she directly asked me if it was for our son. I told her it wasn’t any of her business, which she took to mean yes and she told me I should let him share it and bring it to her house. She has brought this up multiple times since and I ignore her every time. She told me she was going to ask our son to ask me and I told her no, and I would not allow it either way. I said she needs to leave him out of our disagreements too. This was all via email.
My son doesn’t like sharing at his mom’s house because stuff gets broken by the other kids or they hog stuff. He chooses to keep the stuff I buy him with me and use them weeks he spends with me. But I have told him that anything expensive should stay so it doesn’t get broken. I also worry about them keeping nice stuff and claiming my son said it was fine or my ex arguing that the other kids use it more or some shit. I could see her pulling a stunt like that.
She’s furious about the console because it’s a Switch 2 and would be perfect for family gaming, according to her. But I am not buying for her stepkids or her other bio child. I buy for our son and our son alone. Does this make me TAH?