It's stuff like this this gives these kids the upper hand.
You say you have tried kow towing and hobbies.
I think though there may be other things you could do though, @CavaWhoo
Is there any chance that you or your partner could find work at the other end of the country or even in a different country?At any rate, far enough away that they wouldn't be around you.
In the meantime, tell their mum, just tell her that the arrangement won't be continuing and impress that upon her by not being in when they are dropped off. You will have to do this a few times before the penny finally drops.
Maybe threaten to report her for cash in hand and do so if she squeaks.
Go back to the court and formalise custody arrangements that mean she has almost all of the time..
Get a rod of iron when for when they do manage to get over your threshold and , this is the important bit, use it. Take away every screen, food that they don't like. I would say a wash of the mouth with carbolic when they use language you don't like but the police would probably arrest you!
So, make it an unpleasant place for them to be, tell their mum that that custody arrangement won't be carrying on .(If they are with you today, get them in the car and drop them off where ever she may be) and make plans to move far away.
Ignore limp cabbages that tell you they must be unhappy. That's bollocks. Let them be unhappy elsewhere, far away from your small child.