My suggestion is to look at the best ways to invest her house sale money. Nothing pays much interest nowadays but when the money isn't needed soon you can put it into longer-term savings that pay better. You could also consider buying a policy that will pay her CH fees. These are a gamble because if the policyholder dies early then the financial provider wins, but if the policyholder survives for longer then they get the benefit of guaranteed payments. Financial advisors who are members of SOLLA (Society of Later Life Advisors) are the experts in advising on the various options.
TBH, if it was me I wouldn't seek to obtain a gift at this stage. As others have said, small amounts in line with previous gifts would be OK, and if you have any evidence of your mum's long-standing intention to make a specific gift you might have this approved by the OPG. Examples would be: wedding, birth or coming of age of grandchild, once in a lifetime holiday or visit to close relatives overseas. I don't think it is sufficient to say that your mum wants to do it. She's not in a position to understand her overall finances. People often want to make gifts so that the government or other authorities don't get it all, but that's precisely why there are rules about deprivation of assets.
My mum, in a paranoid frame of mind, did everything she could to bar me from having anything to do with her finances, and changed her will to leave me the minimum mandated by Scottish law. Then 2 years later she decided I was no longer a bad person and wanted to change her will to leave me her house. I didn't want this, but my brother tried to progress it, only to find that she was deemed incapax and couldn't change her will. It is what it is.
Not to make any judgment about your own family Tubbsy, because I don't know the circumstances, but IMHO if parents want to give money to their children they should do it while they are still hale and hearty. Waiting until they are already needing to pay for care shows that they either don't understand their financial needs, or they do but are expecting someone else to pay if the money runs out.