I would look into taking some time for you. And don't feel guilty. Being a stay at home mum is one of the hardest jobs ever. Being on call 24/7 takes it's toll on you. I agree with take a personal day. Why should only job job workers get personal days? Mums don't get sick leave and usually while sick have to care for a sick family, AND do all the house things as well.

Checking out is not an option you want for your kids, from how you speak about them. Even if they are the only reason, and it's that way for me, they are worth it.

Old line, but have you tried explaining and begging for family/friend support?

Hope you're ok.