I cant really see what the problem is. I can see you are feeling stressed with the situation, but he is there for a few days a month, so nothing your ILs are doing are holding back his development.
You ask if it would be ok to ask them to pick up 3 afternoons a month, well you can ask but given they don't really drive they probably would rather not. You say it's hard getting ready on these days, that you have to get yours and DS lunch ready, and that he is demanding. Two year olds are demanding, but I notice you criticise your MIL for pandering to his every need! Why do you need to get his lunch ready, does he not eat at ILs? Could you buy something ready made for lunch and dinner those days?
You are concerned for his development. You say he won't feed himself because MIL spoon feeds him, but that she also gives him sandwiches, presumably he is eating these himself. You are worried he can't dress himself. He is only two, he's not going to be independent for a long time.
Do they really not play with him? Does he have plenty of toys and activities he can do when he's there. You are concerned he's not playing independently, I don't think this is from anything they are doing, either he want's to or he doesn't. I wouldn't like him watching loads of TV or phone either. Perhaps take around a load of story books for GF to sit and read to him if GF is not mobile.
I often think that stay and play toddler groups are more for the parents to get out of the house than the children. Not socialising on these days is not a problem, you still have him of all the other days a months for him to socialise.
I can't help but think you are stressed out with DS and or work at the moment, two year olds can be hard work, and you are taking it out on them. No it's not perfect, but then no childcare set up is perfect.
Have you thought about pre school, from when he is three. You'll get your 15 free hours then. You could use these for childcare or to give you a some time off to catch up on things at home