THIS....
It absolutely is the children's money. His children.
Of course he won't like it because he's a selfish so and so who thought he could waltz off and leave you to get on with it and hopefully pay for everything.
But just because he doesn't like it, doesn't mean its better to give in. In your shoes it sounds like it would be better to have the maintenance payments and have more time with the DC yourself and see a lot less of him, with him swanning in as a Disney Dad every now and then.
When someone is so concerned about cutting their parenting "spend" on items for the children as much as possible and then shaving off the contact time too, it really does come across as resentful parenting... so maybe him spending less time with them is a good thing.
But i don't think you should give up hope on maintenance for four children. You are going to need it, to make their lives better.
Every pound he doesn't give them that he ought to will be spent on selfish pursuits and frivolities like tattoos, going by his actions so far.