When I was married and stayed at home (which was for about 9 months) if I was sick enough that I would have called into work then my husband called in sick and came home.
When I was divorced and worked flexible "work from home" work (which was for about 2 years) I would either call my mom and have her pick up my daughter. But by them my daughter was 5-6.... so she could sorta wing it on her own.
I think it's REALLY important to model self-care for your kids. I DO NOT suck it up and continue to take care of everyone when I am vomiting. That just sends a HORRIBLE message to your kids about how important you are..... and about how THEY should take care of themselves.
I also know my body.... If I can sleep for 24 hours I will get over it and bounce back. If I don't.... well, then I'm sick for a couple days.
My sister-in-law used to get up in the middle of the night with her kids when SHE was sick... and let her husband sleep. I've NEVER understood that. I'm all for the "he's got an actual *job* and I stay home" mentality.... but if you are REALLY sick.... then the partner needs to suck it up and let you get better. The same way HE gets to take sick days.... so should you.