It's both intuitive and NOT at the same time. My cat picked up fleas and then gave them to me. Great. Selecting her, the sinks, everything did nothing. So on a whim (and comments here) I bought a random, regular bathtub, placed it awkwardly in my bathroom (penthouse apartment, I am SO hurting for space!), picked up my kitty, and then had the option to give her a bath. Now, granted, I might have had the option to bathe her if I hadn't picked her up, but if you're going to give your critter a cleaning it makes sense that you've gotta be able to hold onto them. XD
Further, I was able to get back my valuable space (and take a shower to get off MY fleas) by putting the tub in my family inventory for next time by going back into Buy Mode. We're all clean and flea-free now, and I'm doubling down on being able to buy a proper house because this damn apartment is too tiny for all of us. :D