I hear you about finances, but any project will cost more than you think.
I have no experience with tearing out a tub and replacing it with a shower in a trailer. I do have some experience with doing that in a residence.
I don't see where water getting out during a shower is a problem. The shower curtain will need to extend below the lip of the shower pan and people will need to be careful as with any space restricted shower.
Keeping the unit water tight will be absolutely critical. Do you plan to buy a TT shower pan?
If not, something will need to be done to fabricate a custom shower pan. Layed up fiberglass over a mold comes to mind, but most people don't work with that. Perhaps you could modify a free standing vinyl shower unit to fit.
Another possibility might be to use a shower system/install method normally use with ceramic tile. For weight saving you will want to use vinyl floor covering or something other than tile to finish off.
Wedi System is one possibility. It is not cheap.
Wedi Shower Pan Sizes | Ceramic Tile Shower Pan Kits
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All in all it sounds like a pretty ambitious project to me. There will likely be many issues to deal with as it unfolds.
Good luck. vic