I don't have an ex, so I can't speak from direct experience, but it does sound to M. like you're giving in on too many things.
Why do you allow your ex time on Christmas Eve, Christmas morning and then AGAIN Christmas night for more presents? Even after taking your daughter to see HIS family for dinner? That's ridiculous.
I think it's worth it for your daughter to have her father around at Christmas, and to visit with her paternal grandparents, but something's gotta give.
If your ex insists on Christmas eve, let him have it, and then offer ONE other time to get together on Christmas day, or suggest he get another entire day to spend with her, J. after the holiday. Ever heard of Boxing Day?
I'd suggest either Christmas morning OR Christmas dinner with his family. Then spend the rest of the time with your immediate and extended family, not his. Maybe roll both events into one by inviting his family over for brunch so he can have "morning presents" and his family gets to spend time with their granddaughter too.
Even if you give in and let him come over for Christmas morning and also take your daughter to his parents house for dinner, tell him to bring anything Santa left at his house, over to his parents for dinner. There's no reason to make an extra trip on an already crazy.
And WTH! Why are you wrapping presents your ex buys for her? That's messed up. He needs to grow up and start taking care of his own relationship with his daughter. If "Santa" is too lazy to wrap presents and have them waiting under the tree in the morning, that's J. too bad. You're not his wife/partner anymore. He can make up some story about how Santa's GPS told him to leave the presents at Grandma's house, knowing she'd be there for dinner...
And despite my rant, I do think it's important to remind yourself that's it's a good thing that he wants to spend so much time with his daughter. Some ex's can't handle it and disappear completely... that said, there's something in what you've written that pegs him as needing to control you in this situation as well.
I mean, why wouldn't you exchange gifts with your boyfriend in front of him? It's your home and he has to deal with your life and how it's changed from when the two of you were together.
I hope this helps. Stay strong and hang in there...