First of all, I am so deeply sorry you have to deal with this sad excuse of a person in your life. He is quite clearly controlling and abusive and nobody deserves that. I am really not surprised his own children do not want to spend the night with him; which in itself speaks volumes. At least they have a loving caring mother more than happy to welcome them home when they can't wait to get away from their awful father.
He is quite clearly taking the piss with this arrangement and he has done it to suit all his own needs/wants without putting the children at the forefront of priority within the proposal of "childcare" (does he seriously think seeing and caring for his own children, is childcare?) I'm honestly confused as to how some individuals survive in this world with their sheer lack of understanding of it.
The times he has proposed for the days proposed are preposterous. The amount fo days proposed is preposterous. It feels like it's to ensure you're getting as little help and free time as possible, in order to restrict your ability to start work at a decent time and have any actual decent amount of time to yourself (again, controlling, which is abusive).
One can only imagine the type of individual his "girlfriend" is, unless she is as naive and blind as is predicted in order to actually date someone of such low moral standing. I do not understand how someone can see someone else treat their own children and mother of their children in such a careless and despicable manner and think it still worthwhile to pursue a relationship with them. Shocking really.
Tell him it isn't enough. Tell him you are not interested in his less than half-arsed offer of being an actual father to the children you both created and send him a proposition back with the dates and times YOU would prefer. A schedule that suits you and your children; who are the priority in this. Kindly remind him the world does not revolve around him, he has all the time in the world to do as he pleases with his life while you carry the dual-burden of single-handedly rearing your children and maintaining your home as well as working to provide for your children while he contributes a pitiful amount each month and seems to think that's his parenting done. Amazing.
If he throws the usual "they're your kids" comment at you that he seems to be fond of and tries all the usual pathetic techniques to escape the oh-so-daunting task of caring for the kids he created, tell him you will therefore have no other option but to pursue to elicit more child maintenance payments out of him, which is the very, very least he can do. Sending money is in no form a replacement of parenting. Remind him of that. £200 a month for two teenage children and one with additional needs is beyond a piss take. He is doing this to put a further strain on you and your finances which is again, controlling and abusive.
Do not let him get away with this. Be confident, be fearless, take no prisoners. Show him your self-worth and know it yourself. Show him his children have worth like you know they do, because clearly he is seriously undervaluing it.
Good luck - you got this