I third that, get her to the vet NOW. A UTI can develop into other major health issues. This needs to be tested and ruled out, or treated. She is also uncomfortable and possibly in pain, depending how advanced the UTI has developed.

Once all health issues are eliminated (and there are a few others the vet can test for), then you have a behavior problem. Cleaning properly is going to be part of the correction. Another is to figure out what is bothering her: is it the baby gate? I can't remember what size dog you have. Some folks with large dogs can set the baby gate up about 4 inches off the floor. Rather than jump over, the cats scoot under. The dog still has a barrier. Another option is to raise the litter boxes - set them on top of a dryer, a chest of drawers. Be sure there is plenty of landing area in front of it. Then the gate can disappear completely.

But the first step is the vet visit.