I have that peel and stick tile ,about 20 of them. Would like to remov

any adhesive remover spray but I always use Google Gone for adhesive you can also take up the leftover residue by using a plastic (Small) scraper wrapped in a cloth

Should be able to pull tile up and then scrap floor

you should be able yo pull them up and if there is residue use a heat gun.

I would restrict the animals from the area while working on removal and replacemen of tile. But if that’s not an option there shouldn’t be anything that can hurt the animals. But you have to make sure and keep them away from any adhesiv!

Use a hair dryer to soften the glue an it may peel away with a little force

Remove what you can starting from a corner or edge. Score the tiles in few places if they don't pull up easily. Then if necessary use a naptha or acetone as many other solutions may not be strong enough and it will become too tedious. Please ventilate as you work-it will say that and give more instruction on the cans. You can also rent a floor stripper, from home depot, but if your bathroom is small you may not want to go to that expense.

I've also read that if you use your hair dryer to heat up the area, that will help with removal.