We quite clearly are not going to cut the total school holiday period, though, and even this petition doesn't suggest that. It's about redistribution, which would be harmful enough to school recruitment in itself. Actually reducing the number of holidays overall would be apocalyptic!
I also doubt any change would improve the clearly insufficient childcare options either. Summer is usually the time when there are most available- I had a choice of twice as many childcare club providers in summer than in eg February or at Christmas. This is because it's usually easier to recruit for longer blocs rather than a week or two here and there.