l wouldn’t let your neighbour stress you out with this.
your neighbour is being ridiculous.
if their child has an allergy that is not your fault. As long as you are cleaning up after your dogs and they aren’t jumping all over the child when you see them then there isn’t anything further you need to do.
I also live in Scotland, unless your dog is being aggressive or mistreated you can’t be forced to give them up.
As are renting as long as you have approval from the landlord to have your pets in the home you are fine. If not and they complain to the landlord that would be an issue of course.
Ultimately it’s a shared area and it isn’t an area that they would be spending a sufficient amount of time in so it’s really silly they think they’d can just demand you to get rid of your dogs. I’d highly doubt it is even your dogs affecting the child if it’s been a year and no issue.
have you spoken to your landlord yet? I know it’s been a few days since you posted this.