Bath tub install with dry wall in place

Honestly, It can be a giant pain in the butt.

You start with covering it with a thick blanket or two and smashing it with a sledgehammer to bust it up into pieces (yeah, that's really how it's done). The blanket is to prevent getting yourself cut up by flying pieces of cast iron and porcelain. You might also have to bust out the tile/brickwork as well, depending on how things fit together.

To get the new tub in, you might just be able to get it in the door, but many bathroom doors in older houses are of the 24" variety and you can't fit a tub through them - especially if it's a one piece shower/tub system. If that's the case you will probably need to take the door out, cut out a stud on one side and bust up the wall a bit to get the new unit in. Then of course rebuild it all once you got the new tub in.

I would strongly consider re-glazing your existing tub. It can really make a crappy old tub look like brand new.

Most tub enclosures, like the one pictured, use a 1/12 to 2" nailing flange down each side and along the top. They are also designed to be used with tubs that have an anti siphon lip along the wall parameter of the tub. It sure looks like you have very little extra relief between edge of tub/tile to the actual corner. In order for the surround to fit snugly to the wall, it must be secured using this nailing flange. I think that you may have to build out the edge of that corner, thus reducing the opening size of the pocket door by an inch or two. This would not be very difficult, but would require some extra finishing work and some changes to door trim etc. If this clearance issue is the same on the opposite side of the tub, the same procedure may be necessary. Also, if you find that your tub does not have the anti siphon lip, extra attention will be needed to seal this joint. If and when you get to the point of tearing out the tile wall, be sure to insulate the stud wall and cover it with a good 4 to 6 mil vapor barrier, tuck tape any joints and the sides and top. This will provide not only water protection, but give you some degree of sound deadening to adjacent rooms. Use only MR (moisture resistant) or paperless drywall to finish off around your new surround. A completely different approach might be to cover the existing tile with a glue on surround kit. Assuming the tile is secure, after carefully cleaning all soap residues and prepping the surface with a dewaxing agent, (isopropyl alcohol for example) trowel on adhesive and install the kit. There are actually some nice surface mount enclosures out there, usually five piece. the box stores typically only have one or two choices and are pretty cheap looking. Check out a specialty kitchen and bath supplier for a much better selection.