My mother is doing alright
Hope it all goes well for her.
As for Mumbai, I can't say I fell in love with the city. I was there with my dad a few years ago, visiting some relatives there before heading of to a beach holiday over in Goa (which was awesome). Pollution levels in Mumbai are high, resulting in pretty poor air quality and of course it's a very crowded and noisy city. The shopping isn't really that great either; most of the international brands are overpriced even compared to the UK (so doubly so compared to the USA) and the window displays are kind of tacky. The local markets are nice if you haven't seen them before, but you will get poor value for money unless you're a veteran haggler. As for getting around, the rickshaw taxis may be cheaper, but have an annoying tendency to break down frequently, so you're probably better off with the taxi cars.
However, there are some nice tourist destinations: the Elephant Caves you've mentioned and some of the historic buildings dating from the days of the Raj. The food varies from average to very good, but I can't instantly remember any restaurant names off the top of my head, sorry. Street food hygiene varies immensely; watch them. If the food is absolutely piping hot having just been fried thoroughly in hot oil and not touched by human hands after cooking, you're likely to be OK, but don't blame me if it all goes wrong!
If the wind is blowing in the right direction and the tide is right, the beach (Juhu, Julu, something like that) is good, though I personally felt our hotel pool was nicer. I guess I have a slightly jaundiced view of the city, given I was only there for about a week.
PS. your assumption about medical care in India for the majority not being at all what you are experiencing is quite correct. You definitely get what you pay for in India! The appropriately accredited hospitals are generally good though, and while I have some quibbles with how they clinically train their doctors there, they certainly tend to have an excellent grasp of facts and the experienced doctors will be solid. The growing middle class of India ensures that the bigger cities are now served by good hospitals for those that can afford them.