Unfortunately, it's extremely difficult to qualify for the Elderly Dependant Relative visa and I've never heard of anyone being granted one before.
You have to be able to show that:
- she has no money of her own at all and is 100% financially dependant on you (and will be for the next 5+ years)
- she is incapable of taking care of herself and needs you and your wife to take care of her physically as well as financially (i.e. help with washing, eating, dressing etc.)
- she has no living relatives in the US who can care for her
- she has no access to any kind of professional care or assisted living facilities in the US and therefore she will not be able to survive unless she moves to the UK
If you can't prove all of those things, the visa will be refused.