Waterproof membrane over Hardiboard needed on walls around tub?
I'm in the middle of a bathroom remodel. It's a simple small bathroom. I installed 1/4" Hardibacker on the floor, including underneath the tub. On the back wall above the tub, (which is an "outside" wall), I installed poly behind 1/2" Hardibacker. Currently the other two walls around the tub just have 1/2" Hardibacker w/o any poly behind them.
In order to ensure it is waterproof and so I use a consistent method, could I just remove the Hardibacker from the two side walls, put up poly, recover the side tub walls with the Hardibacker, then tape the seams (and of course cover the seams with thinset), then tile?
should I remove the polly from the "back" tub wall, put the Hardibacker back up, tape the seams, and use a sheet membrane or Redgard on top of the 1/2" Hardibacker?
Also, IF you recommend using a sheet membrane, is there anywhere to get Kerdi fast? The quickest turnaround I've seen is "we can get it to you in 8-10 days". If I need to get it, I'd like it asap.
Lastly, I'm also going to be tiling the floor. Do I also need to put a waterproof membrane on top of the 1/4" Hardibacker I have on the floor?
I'm a newbie to bathroom remodeling, so I want to make sure that I do this right.