I work part-time and use child care for those days. I fit in chores whenever I can. Is it a hard job working, raising kids and running a household? You bet!
But I think it's impossible to compare who has rights to use care. Some sahm have lots of young children, some sahm need to have their children interacting with other kids for development, some sahm home school and need younger kids looked after, some sahm have high needs children and need a break, some sahm don't cope full stop.
If I couldn't get a spot for child care at the various centers around me, I would have to resign from work. I wouldn't be mad at people who took my spot, I would be mad that there were not enough centers.