I’m so sorry to hear of your ongoing struggles.
This was our situation with my MIL who had advanced dementia but refused any help and a FIL with cancer (unbeknown to us at the time) who was struggling to cope. MIL wouldn’t wash, brush her teeth, wash her hair. And it got to the point that FIL let her sleep in her clothes and sleep in until 3pm every day (as it was easier).
When FIL suddenly died of cancer (he had hidden he was ill) - we were left to deal with MIL. We moved her in with us (as we live quite a distance away and run a business) and very quickly we realised it wasn’t sustainable. MIL refused any help or support which meat my DH (her son) was having to take her to the toilet, shower her - against her will.
After a few weeks (and no sleep or rest bite from the situation) we had no option but to find a care home. We were at breaking point.
We are extremely lucky in that our council (in Surrey) pay for the first month of care. My DH did have POA and although it was against MIL’s wishes he took her into the home for ‘a trial’ he told her. The day she went - there was tears, screaming, refusal but she did have to go in - we just couldn’t cope any longer and she wasn’t getting the care she needed.
Someone gave me some great advice - when the person has no idea of the effect they are having on you, then it is time for them to receive specialist care.
MIL has now been in the care home for 2 years and is absolutely in the best place. It’s a specialist dementia home and she receives fantastic care. The nurses take no prisoners and she is well looked after.
The best place for your mum is a care home. Your poor dad is living his life with a terminal cancer diagnosis looking after her - you will regret that he spent his last months looking after her rather than looking after himself.
Good luck 🤞