As horrible as this is and she shouldn't have called you selfish, because this is an awful situation for you - Nothing would trump putting my children on the street. I just couldn't. Social housing is awful, run down, filled with mould, and private renting is a rip off.
Before anyone jumps on the UC band wagon paying rent - It's capped. They pay up to £700 maximum on private rentals. It's my job to know this. Sometimes they pay even less depending on means tested income (work , capital, inheritance. If you left her inheritance over 16K, then her UC will stop completely. If you left her a mortgaged house like the one she is living in, then she can potentially claim Support for Mortgage Interest.)
Either way, I think if your daughter found herself homeless with children then I wouldn't be expecting her to support you through your cancer journey, because you'll both be in a horrendous situation.
Can you do a 2nd mortgage on the home and increase her rent slightly? Or increase it anyway to get some extra income for yourself? Lump sum from pension? Draw down?
This is a very complex situation to be in. People saying the daughter should have saved - Great. Yes. She would then have her UC cancelled and need to live on those savings to pay rent/mortgage, and then reclaim, but a capital deprivation decision would need to be made, to ensure she hasn't purposely made herself broke to claim benefits.
All scenarios leave them screwed. One major scenario can be prevented by not putting your child and vulnerable grandchildren on the streets. You can have peace of mind knowing they have a roof over their head, they won't have to struggle, you can continue a good relationship with your daughter.
If you do decide to sell, then I think you need to accept that your daughter is also a mother, and a mother will be furious about her children being made homeless. 3 bed houses are in short supply. A privately rented one starts lowest arpund 1300 a month.
What do you want for your daughters future when you are not here and she will still he a single mum?
Good luck with this one.