Shower – what can i do with this old weird tub combo

I know nothing about this concrete thing, but I don't see how that would be an improvement over just cutting away the bulge and then dropping in the insert... and if you're concerned about what's supporting the tub, I'd suggest the right answer is to pull the whole thing, examine/reconstruct that appropriately, and put a new tub in.

STRONG recommendation to get a second/third opinion and estimate.

This is almost certainly not covered by insurance -- ordinary repair is the owner's responsibility -- unless you have a "home warranty" policy in effect from when you bought the place.

I have done almost this exact same retrofit. It was a lot of work, but you can leave the existing tub. I refinished mine with a Rustoleum epoxy product, but that's another story.

Basically, depending on the tub, I would take everything down to the studs, and start with a good masonry board, and any possible structural/plumbing changes you might need.'

The important thing is to make sure when you are all done you've accomplished two things:

1. A good, consistent seal from the tiled surface to the bath tub
2. See No.1

I've repaired and refinished bathrooms where this was done, and 9 times out of 10 there was water penetration around the bathtub that caused unmentionable horrors that were invisible, until it all failed horribly.

Good luck and take your time.

PS - a "zip saw" or handheld router can be your friend to cut that modular shower into smaller pieces.