As a mother I had expectations, there was things & wanted and did want, concerning my DC. As many parents will tell you, I may as well have been talking to a brick wall. It's a GP prerogative to do what they want.
Here's the bit to focus on, as long as the GM isn't letting your DD do anything logically dangerous. (Ignoring how hypothetically a bag of sweets or CBeebies isn't what you'd do) A GP is likely to think oh DGC deserves a treat.
If you were fed up with everything after DD1, why oh why get yourself into a situation, where this man Father’s two of your children. In your head you might have spent the pregnancy and beyond, thinking what you would do this time.
I would listen to PP who have said the police might take a dim view on the fact you're calling them due to whatever cause, they might refer to SS, as if we can see this as being unreasonable behaviour, do you think the police are going to be full of the joys of spring on the 20th call.
I'll make it a tad clearer, if they involve SS & if you are assessed as having a problem, the Grandparent may be rewarded more hours, if not possibly even more contact than that, as SS may query if DC's Father behaves as he does to please you, the Grandparent is assessed as being a normal Grandparent. The main issue is you not liking her. Since the beginning of time MIL's & DIL's haven't seen eye to eye.
It's not giving in, it's giving each child access to their paternal family.
From a family funeral I recall a situation where a child asked a relative, why don't we see you? The relative couldn't really say, well your Mum is bat shit crazy, her word is gospel. DD1 might be asking the GP why can't I see you more, why this, why that. The GP isn't going to lie and say well I only want to see you for this long.
I'm really hoping this is sinking in.