To be honest, as your father in law is not going to do anything about spaying the cats, perhaps you could do it yourself. It seems like the only viable option.
If I was in your situation I would save as much money as I could every week and get the three girls neutered, by using vouchers and money of your own.
Then just contact as many animal places as possible to get them to take the kittens. Even if it means taking them in a cardboard box on a bus there.
I'm sure somebody will take them from you.
You need to make a decision of your own and forget FIL cause he's obviously some kind of arse.
It's stressful, but it's more stressful having kittens all the time, and it's not fair for the three cats who keep getting pregnant or the kittens who may not find homes and have to be put to sleep cause there's too many of them.
I think I would take it upon myself, put my foot down and sort it without him.
If he doesn't like it or disapproves it's tough, take no notice, You don't want ot be listening to people like that cause they don't know what they're talking about.
I think you'd be doing a wonderful thing, if you did get them spayed and got an organisation to take the kittens. It's in your hands, and you love cats so if you can do it, then go for it.
I wish you good luck and my thoughts are with you trying to help these cats.

Kate