Yeah, blood work and perhaps a urinalysis should be done. I hope there's nothing wrong, but it doesn't hurt to check. That bunny's bum looks like a bunny I petsat who was too tubby to reach around and clean his own butt. He would get cecals matted around his urogenital/anus area, and poop and pee into that matted area, so that the poo and pee couldn't get away from his bum. It was like a pocket made of cecals with poo and urine inside it. I made a thread previously, but retracted it because I asked the owner to join the forum. They haven't joined yet and it's been several months, so I assume they're not going to. He had a spinal deformity plus a lot of extra weight on him. I don't think he and Kate have the same issues, but that skin is pretty irritated from the urine and feces. I would wash him daily, usually in the morning because that's when he'd have his cecals that he couldn't eat. Then I'd put Udderly Smooth on the area in an attempt to soothe it. I have heard of using baby diaper creme or Preparation H in the same way to soothe the skin, and also baby cornstarch.
For Kate, of course she needs blood work, urinalysis. Does she move well with her back legs? For instance, do you think there might be a hind end paralysis issue? That could contribute to sitting in pee and peeing everywhere. If so, have the vet check her spine for fractures, arthritis, deformity, and also it might be good to check for E cuniculi. That often presents first as a hind end paralysis and urinary incontinence. Puppy pads are good, and Autumn's statement about the litterbox being a different texture etc makes sense. It also might make sense to have her in one of those dreaded wire bottom cages, but with a board to rest on, at least until she can get her litterbox habits together.
