It's very, very important to remove all of the urine odor from the home in order to re-litter train the cats. You're going to have to scour the floors and wherever the walls were splashed, and likely replace/remove the carpets and scour the floors underneath.
Homemade Urine Cleaner:
Equal parts White Vinegar and Water to soak the area that had urine on it, whether it's an old dried up spot or recently wiped up spot. Let it soak in to carpet or sit on concrete; spray on the wall area; wherever there's pet urine. Let it really get in there and then blot it up with paper towel as much as you can or soak it up with one of those clean machines like a SpotBot.
Then sprinkle a pile of baking soda on top of the damp area where you just lifted the vinegar solution.
In a spray bottle, mix a cup of 3% Hydrogen Peroxide with a teaspoon of liquid dish detergent that you would wash dishes by hand with. Spray that onto the baking soda pile or drizzle it. Spray it onto walls. Basically, make a paste.
Scrub that paste into the area with a toothbrush and really work it in. Let it dry. After it dries, vacuum it up. Scrape up stubborn pieces if you have to. The stink should be gone, and your cats shouldn't be able to smell it either.
The only urine smell they smell should be in their litter boxes, so that "should" be the only place they urinate.
EDIT: I do have two cats and we live in a house where the previous owners had cats who urinated and defecated in the basement, so guess what our cats do? :-)
EDIT AGAIN: Cats don't actually have "sensitive" stomachs. What they have is an intolerance to the fillers that are used in cheap kibble and the acidity in the gravies of wet foods. They need kibble that doesn't list corn meal as the first ingredient. They need kibble that lists real meat and has other healthy ingredients. They also need to have wet food once or twice a week to make sure that they're not getting dried clumps of dry food causing blockages in their digestive tracts.
They also need to have their fur brushed regularly to avoid swallowing so much that they're vomiting up hairballs. In addition, you don't have to give them hairball remedy or special diet for hairballs, but put dabs of Vaseline on their paws once a week (which is the exact same thing in the hairball remedies on the shelf that you pay $6 for a small tube for) and it helps the hairballs glide out the back end instead of being vomited up the front end.