Looking for some insight on best approach for prepping a floor for vinyl plank install.
I am laying down vinyl plank flooring in our laundry room/mud room. I was going to remove the two layers of peel and stick flooring first. A contractor coming in to liquors painting kitchen cabinets mentioned he would just put it over the peel and stick.
My instincts are to remove all existing peel and stick. But my wife says I have a tendency to make projects bigger than they need to be. 
Flooring – Safe to install vinyl plank flooring over existing peel and stick
flooring
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I'd question how waterproof you need this to be. Will there routinely be water sitting on the floor? If not, you may be over-engineering things.
That said, off the top of my head, one option for waterproofing the subfloor would be to paint on Redgard:
It's a 'paint on' waterproofing membrane that you'd typically use behind tiles on cement board and the like.
They are waterproof in that you can get the top as wet as you want. They are not waterproof in that they will keep water off your floor, nor will said water not affect the bond to the floor. These tiles may be able to last sitting in water but they will not keep water from getting underneath. Your only options are really one sheet of vinyl or tile (could I guess use a membrane).
If you install these right though I would bet that 99% of the water (given you don't just let an inch of standing water sit) will never meet your subfloor. No caulk is needed, just make sure that all of the edges are tight and clicked into place. To keep your bathroom better suited for a kid you may want to make sure baseboard are sitting right on these and caulk between baseboard and tile.
Best Answer
Floating floors like that were developed specifically to avoid the need to remove the flooring underneath in most cases. if your existing flooring is well bonded and flat, there's no need to take it up unless you have height transition issues with adjacent rooms.
To be absolutely sure, and to avoid compromising your warranty, read the product literature.