I'm guessing you don't like cats. Which is your prerogative, but means you've no idea what you're talking about.
@notaurewhatusername You absolutely can have cats with a newborn, as long as the cats are looked after correctly - which unfortunately is not the case here. Cats need space, clean trays (1 per cat +1) which are spaced around and not near their food or water. Impossible to achieve when 4 cats are cooped up in two rooms. Especially when they don't all get on.
The trays need to be scooped as soon as they are pooped, and cleaned regularly - trays washed and fresh litter put in. Cats can be fussy about the type of litter used; try different types to see what works.
You say 2 (?) of the cats are indoor only, but you have a cat flap for those that go outside - how does that work? Is the flap locked to contain the indoor cats, or do they not want to go out?
Cats need to play to reduce boredom and stress, do they have any toys, does DH interact with them at all? You don't need expensive tatt; a stick with a long piece of string to wave around, scrunched up paper, crisp packet tied into a knot, or a cable tie they can chase.
Cats love to climb, a cat tree (with scratching posts) is a good investment, and shelves they can jump onto.
A pp mentioned UTI being a possibility. Get the cat(s) to a vet for a checkup. If you've ever had a UTI you will know how unpleasant they are! It can be managed, but first it needs to diagnosed.
Your DH needs to step up, now. These are his pets and he is not looking after them correctly. But no, you absolutely cannot rehome them without his knowledge.