Prioritising the DVLA is, as you have realised, an absolute priority.
These situations are always so very hard. One thing to be clear about is that if a major life change, like a house move, is to happen, you need to plan for this to cause a deterioration in their functioning ability. People with, or just developing, dementia often function by the skin of their teeth when they are in familiar surroundings, but a move makes things worse.
This is not a reason not to do it, but you need to be very aware of this.
They could move to sheltered or a bungalow, deal with the deterioration, eventually get used to the new place, where everything is, routines etc. and then finish up needing a second move to residential or nursing care as the condition deteriorates.
My thoughts would be that initially it might be best to put in maximum support for them in familiar territory. The Age Concern website will give you lots of advice: www.ageuk.org.uk/information-advice/care/
At the point where this is no longer viable then they could look at a move to residential or nursing care, possibly nearer to you. In this way they only make one move, because the strong likelihood is that if they moved to a bungalow or sheltered accommodation now, they would eventually need another move to residential - two moves is too much.
I used to work with people with dementia.