Poor you. And your poor mum. My situation was different as my father had effectively hidden my mother's growing memory problems before he died. My mother was in denial so it took a crisis to dislodge her. Your mother, by deciding to move now, is doing you a big favour.
It must be particularly hard for your mother, for this is her home, her possessions, she is presumably grieving for the husband she has lost whilst looking after someone with dementia. The endless questions, the mood swings, things forever being mislaid, the fact that you discuss things one day and then the next day the agreement is forgotten so you either discuss all over again or are accused of going behind their back.
This is the time to be there for her. However awful the task, there is a huge satisfaction to be gained from doing the right thing. My brother became invisible, not unexpected as the same thing happened when my father was dying, and not unusual. Though I could have done with some help, or at least some supportive noises, I feel he has missed out on the important experience of getting close once more to his parents and understanding more about where they, and we, came from. I am also felt the experience has help my own children understand the importance of family.
In practical terms I would suggest that you focus on identifying on the minimum day to day stuff that is needed going forward and getting rid of the stuff that is genuinely not wanted. Other clothes, china, photos etc can be packed into boxes and kept in a garage or somewhere. Then when the move has happened everyone is less stressed you can get the photos out and go through them, involving your dad as well.
I sat my mum down on a bed and went through her wardrobe (actually she had spread to five wardrobes...) and tri-arged her clothes. Everyday, special occasion, and to be got rid of. Great piles on the floor. She is still sure she is going on a cruise this summer. The everyday were unpacked in her new flat before she left convalescent care,and the "cruise clothes" are wedged into two suitcases which she has not asked about, and which in due course can go. The rest went into one of those recycle bins at ASDA. It was not much fun but we did it in a day. Selecting key linen and kitchen equipment were done in another day. (Easy, four sets of sheets, three saucepans, six sets of crockery and cutlery, one kettle etc...)
My mother had agreed that she wanted less clutter, and indeed seems to enjoy her more streamlined flat. Luckily she was not around to see me go through the rest. The back was broken when my husband came down one weekend and we blitzed it. Is there any way your mum might agree to them staying elsewhere for a weekend, or is it possible for them to move first with key stuff and leave you to sort the rest. Or would she find this too stressful/upsetting?
The manager of her sheltered housing said some couples actually leave the lot behind and simply go into John Lewis and buy new furniture suitable for their new home. A nice idea. Equally others pile everything into the spare room so you cant enter, having thrown nothing away. Though apparently this then often gets cleared bit by bit as people realise they dont need it.
Momentos are important. Especially for your dad who might need key pictures or ornaments that they have on display now to help him orientate himself to his new home. I was told to expect my mother to take a couple of months to settle - and indeed now two months later she thinks she has been where she is for a long time, but there was a noticeable difference when I brought over things that were important, and a display case for them to sit in.
Sorry it is again pretty long. I am so pleased to have got my particular challenge over with. I dont envy you. One thought that sustained me was that it would have been much more difficult if I was clearing post funeral and had no chance to understand the significance of various things, including the linen which my grandmother carefully hand crocheted, even though my mum is quite hit and miss about remembering where things came from. Difficult as it would have been, I wish they had decided to move, and to have asked for my help, when my father was alive.