"Seriously, what is the increased risk of a person living in a single residence household solely mixing with another person living in a single person residence?"
It's hard to believe that 7 weeks on this still needs explaining...
Every person you see, sees other people - so you go to the supermarket, the corner shop, pass the the neighbour, pass too close to a couple of runners ... all a risk. (Say 15 people in a week)
The other person does the same - but with different people
Then you meet up and your risk is now from 30 people ... not 1.
This is a meaningless and silly 'explanation'. It is EXACTLY THE SAME if 2 people live in one house.
OP, if you and your mum are both single people living alone in nearby small houses, then I cannot see any reason why you cannot become a single household. Just because your bedrooms are further apart than usual doesn't change anything.
It is very comparable to the 'one household' example of DC moving from one parent's house to another parent's house where parents are separated, except in your case it is far safer.