Really? I understand being upset that you'll be short a teacher. But to be upset with the co-worker. She is making a decision to do what is best for her. You have the ability to make the same decision.
Sounds like the work conditions are very stressful. I would find another job too. Your work does not have to be this stressful. I know day care workers and tho they have stress they love their job. I would want them to quit if they didn't at least like their job. I would remove my child from the situation you're describing.
I would stay out of the process for your co-worker. How she quits is her business. She may not even quit and if you "give the supervisor a heads up" you're adding to everyones' stress.
I urge you to focus on doing what is best for you and let other's take care of themselves. This will reduce your stress level.
BTW If this place is licensed I suggest that they're not in compliance. If it's not licensed I wouldn't work there or send my children there. For one reason, if she's not licensed she is breaking the law.
If you want to do something about this situation, find out if she's licensed and what the rules are? You can find out about the rules on the Internet. Google your states department of human resources. You can give them a call to see if she's licensed.
I would definitely start looking for another job. Good workers are in demand. You will be protecting the children and other workers by finding out about licensing and rules. It is not your responsibility to continue working at a center to protect children. When workers don't stay, it's a heads up to the parents that this is not a good place. By staying you're allowing the owner to continue to mistreat children and staff.