Long Haired Cats VS. Crawling Baby?

I have 2 long haired cats. Besides the usual shedding issues, they also have quirks that I consider to be extremely unsanitary. One of them eats WAY too fast, and vomits (We've taken him to a vet, and there is nothing seriously wrong, he just eats too fast). And the other has recently decided to pull terds out of the litter box, and bat them around the house. I dust and vac 2 to 3 times a week for the hair. That I can deal with. However, the sanitation issues with the poop-play, and the vomiting is really worrying me. I can't imagine letting the LO crawl on the floor in the living area (which is where the cats live). They get litter everywhere too. What happens if LO eats bits of litter?? I love my kitties, but I am at my whit's end here... I am thinking that the only thing that makes sense is re-homing the kitties, but they are so sweet.... I am so saddened to even have to think about this, but I feel it may be necessary for my LO. Has anyone else had to do this? Please give me some advice, or support. This is a tough thing. I'm not sure what I will do.