You have a lot of stress on you right now, UGH!
What about a deadline?
Why not set a deadline for yourself, that if you have 3 kids undercontract for daycare by July then that is what you do.....
I would make the people sign a contract (an agreement for services which includes rules and expectations for both sides to keep communication clear) to protect yourself and them. If it is only a few children, you don't have to be licensed. I would google and look for a contract template as well as policies/procedures and hand them to the parents with a signed contract. You have to protect yourself.
You can enforce the contract in civil court under 'breach of contract'. One consideration might be to look at how reliable this income would be? If the people are changing their mind so often? I sounds like you want this to be your ONLY income, not supplementary?
If you don't have 3 kids or whatever number you need, then take the teaching job for one year. First make sure your childcare expense (your kids) is worth the salary you will be making.
Like the other post said, advertise in churches, etc. One nice thing about home day care is when school is canceled (inclimate weather) the day care is usually still available. This past winter everyone was hit bad and the schools left working parents stranded.
Good luck with your decision!