Fellow SM here.
I see so much of this shit on the SP board.
As a SM you are seemingly expected to all/any "parenting" that benefits the actual parents but are considered to be the devil incarnate if you over-step (pun intended) this magical line where you assert your (and your children's) own perfectly reasonable boundaries.
I made clear from the start with DH that we had house rules (and consequences) that applied to all.
Simple expectations such as good manners, respecting other's privacy and belongings and doing age appropriate chores.
Break the house rules and the consequences are the same regardless of whether DH or I dish them out.
In the same vein I have never been free childcare. Of course I'll support/help in an emergency but when SC are here the expectation is so is he (and he always has been - again bar rare emergencies - because that's kind of the point).
The idea that you can't pull your SC up on taking you for granted and being rude as hell in your own home is ridiculous.
You need to down tools and have a total reset.
Starting with next Tuesday. Go out. Be unavailable. His DD will have to go to the sport fixture or stay with mum.
Stop making pack ups. Frankly they are at an age where my C and SC were making them themselves the night before (with some support and DH/I would make sure the appropriate food was available).
Tell your partner you are doing NOTHING until he starts to parent and you establish some basic house rules/expectations and consequences.
If he can't be arsed to do that now he will be doing all of it in the future because you'll be shipping out permanently.
You are being treated appallingly by the 3 of them. Find your backbone and stop being treated like a nanny with a fanny as a pp aptly put it.