Is this the same poster who posted about an extra similar sounding property a couple of months or so ago? They also had a 12y and lived in a small 1 bed flat, though that was a ds not a dd iirr.
I thought council properties went quickly but, if same person, this dilemma has been going on for 3 months.
You say the rent and location work well for you.
Op - you're sleeping in the living room and kitchen where you are. Surely you don't want to continue with that.
I'd have thought a 3 storey maisonette must be better than what you and your child have right now.
You're excuses for declining are pretty weak:
Cleaning the stairs - get a handheld cleaner.
Accidents on stairs - almost all houses have stairs, unless a bungalow or another flat. We have a 3 storey and we aren't regularly having accidents on them!
Resell - you're not planning on buying it. No one would force you to buy the property if you decided it wasn't your dream home anyway.
Toilet on ground floor - admittedly annoying but it is still a better home than you're current setup ime. You're both young and able it seems. You'll adapt to it quickly. We didn't have an upstairs bathroom growing up - it was a non issue.
Security - ring door bell and/or camera, chain across door as well as always keeping the door locked. Burglar alarm if possible - can set it so it's in at night but only in ground floor and windows for example.
Fear of the unknown - well that's going to be the same regardless of what you're offered.
Unpopularity of townhouses - well, it doesn't sound like a townhouse, more of a maisonette. However, regardless - townhouses sell well here and have remained popular. Where I live they sell quickly and for above asking price.
If you decline, you may be waiting another few years for anything more suitable. You've already declined two properties - will they even keep offering you more and more?
I'd accept and enjoy having much more room, with better privacy for both you and your child.