From experience, working 4 days a week can be brutal - I guess it depends on your employer and your husband, but I know many women who have said the same. This is particularly the case if you have to schedule all medical appointments etc for one day a week.
It might be okay for a job where there is absolutely no prep work required. In my case, my management was shoehorning the work from my 'day off' into the 4 days I was on the premises.
I don't think that that could happen in the OP's current role, but she should bear this in mind - and the difficulty of organising all appointments for one day still stands. By the time I went down to a 4-day week I was only looking after my husband. The OP has 3 family members to take into consideration, so harder to juggle.
In my case, my SLT simply re-allocated the teaching load for my 'day off' to my other 4 days and left me to sort out all the managerial tasks for the 5 days. Super... Legally, they could do that since the actual regulations only specify the minimum non-contact for a teacher - there's nothing set in stone for middle-managers in Scotland.
After a year, I asked to go down to a 3-day week and was refused.
I know at least one person in a non-teaching role in an English secondary who found herself in very similar position.
As discussed in many previous posts, the OP would still need her husband to take on the management of many of the household related tasks including appointments for the children.