OP I am glad you seem to have a way forward now. I assume you are not of Indian origin as if you were this is one of the things you should have known about and talked about before you married.
There are a lot of pretty shocking comments on this thread. The MIL is not cheeky to assume that her adult kids will help her when she becomes widowed. That is how things work.
For many married women of her age with kids, getting paid work was extremely difficult in most of India and carried a lot of stigma when she was young. So no, she probably had little financial control overt her income or lifestyle. People are looking at this through 2019 western eyes. In many parts of India lone widowed women have very low social status and can not get paid work. Various charities run schemes where widowed women can work and survive.
So simply returning to India and living off any money she earns/has, probably is not possible. It could literally mean you are sending her back to live in a shack and struggling to eat. Even if things are not that dire, the chances are that as a widowed women living alone she will have very low status and be socially shunned.
So of course her son wants to make sure his mum is okay. Its not about being frail or needing care, its about being in a reasonable living situation.
But the OP also wants to live a decent live and does not want to have to share a house with a virtual stranger who expects her to do everything.
She probably will not get a permanent visa for the UK anyway. But a granny flat either with you or SIL is best bet. You may all have to pitch in financially to enable that to happen. I agree that travelling back and forth between the US and UK is not sustainable except in the short term. Lots of health conditions mean you can not fly long haul, so this may only be possible for a while.
Also agree that wherever she lives getting her involved in the local temple, gurdwara, mosque, etc is the way forward. She will meet others and be able to build a life for herself.