busybea, welcome, yours is a real dilemma. If it was just you and you are so unhappy where you are I would think moving to be near your daughter was sensible, but it isn't that simple as you have your mother in care in London. Would your brother visit her more if you moved? Does your mother still know who you are and enjoy your company?
The Bristol Housing Association sound very proactive and willing to help. Perhaps next time you visit your daughter you could ask them to show you what kind of accommodation is on offer and discuss the weekly visit they make to tenants. It may feel intrusive but it means if you need help of any kind or there are problems with the flat you have someone coming in each week you can tell and who will make sure the problem is dealt with.
At 61 you probably will find that most of the other tenants are older than you but they are all obviously able to live independently with a little help so you may well find that they are mainly mentally and physically active and may share some of your interests.
As for work, with only a year or so before you reach retirement age, it really doesn't matter what you do as you will not need to do it for long. If you moved to Bristol any work would help you get to know the town and people in it.
I think you need to investigate all the options, carefully and then write a list of pros and cons of moving to Bristol or staying put, or perhaps moving but not before you reach retirement age for example. Seeing it in black and white on paper can be very helpful in making a decision.