For the record: I was around in the 60s, and I’d have hated all that pink just as much then, as now.
If there is another tub in the house, consider changing it to a shower stall, preferably with a foldable wall-hung seat. While there are times I’d kill for a bubble bath and a tub can make handling toddlers much easier (the toddler can’t run away), showers are much more accesible for most people. The seat makes it easy to perform footcare or for a person with mobility problems to take a shower and, unlike a chair, it won’t slide away.
Is the tub cast iron?
If so, forget trying to re-glaze - I’ve never heard of anyone liking the result.
Find an ape of a young man, provide him with gloves, face shield/goggles, and a large sledge hammer - the pink will be a pile of rubble within 20 minutes.
If you don’t move any fixtures, you might get away with just dropping in replacements for toilet, tub, vanity, and lavy.
If you run into rusted steel pipe, your $2000-$3000 estimate just might prove a bit on the low side, unless you can re-do with copper yourself
If you use MR rock, you can get away with setting new tile directly on it. It may not meet code, buy my work was still standing after 20 years.
CHECK CODE before removing the only bath tub - when I looked at it, EVERY house had to have at least 1 TUB - just for the very young and very old - you don’t want to get ready to sell and having every agent tell you that you will need to either put in a tub or sell “as is” - which means “knock 10% off your price”
Is it just me, or is anyone else dying to know what happened to the pink bathroom? 