Alonsos, point one, really your husband is breaking the rules. The supermarket own that land, it is theirs to do with as they wish. They choose to provide those spaces as parent and child spaces to make life easier, and to make things safer. Your husband breaks these rules when he parks there.
If however he was using his blue badge then fair enough, no rules broke as he can park safely where he needs to. Without using it then technically yes he is breaking the rules.
A similar comparison would be to me, as a car user I don’t park in a bay designated m/c (motorcycle), as whoever owns or is responsible for the land has designated this space as for use by motorcycles to park only, not cars. Rules are rules I tend to stick to them. I don’t twist it and justify it in my head and decide that for whatever reason I have the right to park there.
Point 2, ok I said mums with babies/small children. In the same way the supermarkets have generalised and said parent and child.
When in fact you are totally right, it could be mum, dad, grandparent, aunt, uncle, older sibling, babysitter, nanny, foster cater, great aunt or uncle, family friend, au pair, or many other adults who are looking after a small child.
But to save myself the hassle typing, I just put mum, assuming that most people are well aware that like ‘parent and child’ mum and child is, when discussing parent and child bays, an exchangeable term for another responsible adult.