Hi,
I have just read your post and I think that you are fantastic neighbours and deserve the utmost credit for what you have done so far. However, having been on the "other side" as it were I can only say that my mum fought tooth and nail not to go in to residential care. Despite neighbours and carers and even the local Vicar telephoning me and expressing concern about her condition, she had not been fit to live alone for over twelve months. It is very very difficult because unless you have "Power of Attorney for Health" or have your loved one "sectioned" or declared unfit to make a decision in their own best interests there is very little you can do about the situation.
We had organised carers 4 times a day, overnight carers and were visiting and supporting mum, who also suffers from MS, as a family. The "Car finally crashed" after several falls, Hospital stays, telephone calls and texts from concerned carers,visits from Social Workers and Doctors that mum agreed to go in Residential for two weeks respite. This has since Xmas developed in to permanent care and she is fast deteriorating, as a family we feel guilty that we have had no option but to over rule her and have her admitted to permanent care but realise that we had no option. We have lost the fiesty lady who used to dictate her terms (and ours) and this is heartbreaking as she will never return home. Having said that we were losing our own sanity with the situation as it was. The worry and constant anxiety we suffered when she lived alone has been replaced by the worry and anxiety that she is now unhappy and deteriorating, this may have happened had she remained at home we will never know.
I can see both sides of your predicament and can only say that we were paying nearly double the cost of Care Home fees for private care (self funding) and mum was still falling and suffering anxiety attacks in between care visits, the carers visits were sometimes up to two hours at a time. Social Services care is means tested so possibly your neighbour is not self funding, I wouldn't like to say.
I think you may need to take a step back and allow the family to deal with the problem. I fully understand your concerns but unfortunately, as in our case, I feel it will take a fall or an illness to bring things to crisis point before the situation is resolved. Perhaps your neighbours family are relying on you a little too much I can understand your concerns and by all means make those phone calls if you feel you should, be supportive, but there is a point where the family will have to take responsibility and act in her best interests. (You cannot do this.)
It is such an awful unpredictable illness to which there is no simple solution.
Hope this has helped in some way.