I never ever saw my Dad on xmas day as a child (stepmum didn’t and I absolutely did know my gifts were much less.
Stepbrother would be sat next to massive pile of stuff he’d got while playing on the console and ten games to go with it all bought my Dad while my brother and I opened a book and a cd. I never complained, and thanked stepmum and dad for the few things I did get but I won’t lie and say it didn’t hurt. I found out after his death it was because stepmum felt her son should get more to make up for me and brother getting two Christmas. My Dad left my Mum in the shit finance wise, he didn’t pay maintainance half the time, and when he did it was £5 a fortnight (and he did everything he could to stop that). Stepmum said I’d already gotten gifts off my Dad as he paid my mam £5 a fortnight, hahahaha.
My Dad lived ten mins away and couldn’t see his two children on xmas day because he was “busy” watching stepson open gifts, that I was selfish for asking him to come and pick me up.
It was never about the money, or the size of the gifts etc, it was about the presents being yet another thing showing how I didn’t belong, how I was a pain in the arse esp for my stepmother, and how I was seen as less.
I had very little gift wise off my Mum, but loved xmas with her, she did her best every day, with very very little help from my Dad. I was wanted and loved. Can’t say I felt that at Dads, not just at xmas but all year round.
My situation is different in that my Dad was the one buying the gifts, that he earned decent money yet chose to not support his biological children and watch them go with holes in their shoes while he bought his stepson expensive trainers, it wasn’t a case if stepmum paying herself, or her ex paying for his child (he wasn’t around)
I think if you live together then you’re one household. You’ve gone from two single one child households to a couple with two children. The nine year old is a child and sounds like she needs some support, and your partner need to deal with his child’s behaviour, it’s called a blended and when things blend there’s changes on both sides. You need to discuss which changes need to happen so that you’re respected in your home and that his child feels as much part of her fathers family as everyone else who lives with him
Good Luck OP