My kids have been in daycare awhile now, and it's a pretty hard and fast rule, that if they're sick, they are sent home. There's a 24 hour rule for fevers, and if they have even a little fever, they get sent home, and can't come back the next day. Same for diarrhea. (Including the time the daycare provider gave him pizza when he was 1 and it gave him diarrhea...) I try to keep them home if they're sick so germs don't get spread to the other kids, and I hope the other parents are doing the same. Even when they don't have a fever, the day care has called and said to come pick them up because they're not feeling well, just want to lay down, etc. I was given about a one-hour grace period from the time of the call to come and get my son.
Is it inconvenient to be called in the middle of work to come pick up the kid(s)? Sure. Is my boss excited when this happens? Not really. Do I still pay for the days they are excluded for being sick? You betcha. But, you know it's the kind of thing that happens sometimes.
After my son turned two, and the kids were pretty much the same in daycare give or take, we had sort of all gotten accustomed to each other's germs and no one was getting sick as often.
Also, I know there's a clause in my contract with my day care provider that says the relationship can be terminated by either party with 2 weeks notice. If it's causing a problem with your family, as well as the running of your business, those are the breaks. Maybe give a month or six weeks' notice to give them a chance to find another arrangement. I don't know exactly where you're located, but with the lack of infant care availability in this area, I have a feeling you'd fill that under-2 slot pretty quickly.