The whole plan with what you have to work with is wrong.
A drop in tub is far more likly to leak under the lip around the top.
Carpet never, ever should have been installed there in the first place. A sire way to have mold and rot under it.
Going to have to remove the tub to be able to do tile.
By the time you add tile board and tile it's going to be to high around the tub if it's left in place.
If you really want a shower you would be far better off getting rid of that whole tub and installing a real tub and shower.
When you remove that carpet if that was original to the home, I'd bet your going to have rebuild that whole thing to make strong enough to support tile and not have it crack.
If they just used patical board it's all got to go.
Other things not withstanding, How are you planning on keeping the water IN the tub? The only way to do this is with a round curtain system like you see over the old clawfoot tubs.
I have one of these in our guest bath. It is such a pain in the back end I let house guests use the shower in our master bath.
The curtain is clammy, it grabs you, Not to mention there is absolutely no where to put your shampoo or soap.
I would seriously rethink this.
Even if you manage to do this, you won't be happy with the results.
To say nothing of the free-standing water supply pipes and shower head. Just not a good idea at all. Trailer homes are not constructed substantially enough to support most tile installations. The wind blows and the grout cracks.
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