So his "sensitivity" about his daughter is conveniently controlling you in your own home?
How convenient he has found a woman willing to move, change job, pay 50/50 for a house that is dominated by his child.
A skivvy aupair type that cleans up after them too.
So convenienOPfor him OP🙄.
He must be delighted with himself.
I fail to see what you are getting out of this arrangement, thats for sure.
You have given up an unfathomably amount for him.
This is your life now and will be only worse if you have a child with him.
His priority is his child and you are simply an instrument for her comfort/housing, skivvy cleaning.
Give some thought to your future because it doesn't sound great from the many many threads on MN that are similar to this, but further down the line .
These guys always find a solvent women to provide housing for their children.
Give some serious thought to what you want for yourself.
I can tell you one thing....women with self esteem give guys like this a hard swerve.