i'm still call myselfm technically a SAHM, even though my kids are now 15 and 18. The older one is disabled, i am his legal Carer as well as his parent. I'm also an unofficial carer/companion for my elderly mother.
When both were in school full time that time was spent doing EVERYTHING, cleaning, prepping meals, laundry, life admin, taking mom shopping, taking her to the bank, helping her with her housework/diy, doing my shopping, my banking. taking both of us to various medical appointments (i'm also disabled)
I also used the time for respite and would have an afternoon to myself to sit and read/chill with a coffee somewhere, because the minute they were home i was back on Carer duty.
He's in college 2/3 days a week currently, so same thing, the days when he is home i'm in Carer mode, but also doing all the school runs for my other child who is also disabled (asd/adhd), so currently also helping her with GCSE homework/revision every evening.
Its really off to say 'you're not a sahm if your kids are in school' if you have zero idea what its like having disabled kids and an elderly parent to look after.