Late to the party, but better late than never.
I have upgraded several mobile homes and RVs to residential sinks, lavatories and faucets. Often the good Delta faucets won't fit on the holes where the RV faucet came out, so I wind up replacing the sink and under-sink drain plumbing while I'm at it. That often means cutting a bigger hole in the counter where the sink or lav goes. Study the current cabinet to be sure you can cut out a big enough hole to install the new sink/lav. You may need to replace the cabinet too.
Replacing a shower/tub with a residential unit should be no big problem for a good DIY person. Just be sure to measure the hole it must fit into before you buy the replacement. Then during installation, always measure twice, cut once.
Also measure the door(s) the new unit must pass thru to get to its space in the bathroom. Even on a stick-built house, some showers/tubs won't go into the bathroom without tearing down a wall or two. On new construction, notice that the big tubs/showers are placed in the bathroom area before the walls are built.
If you are replacing the original shower base or shallow tub with a new base, remember that ceramic tile is very heavy, so plan to stick with plastic shower or tub stalls that will work with the new base. Glass or mirror shower doors are nice, but heavy. So plan on using a shower curtain instead.