Multiple LLC's with parent and subsidiaries
First of all I agree with your attorney that each of your day cares should be organized as a separate LLC, to limit it's liability to itself.
Second, you could have a forth LLC registered for the purpose of providing workforce to those other 3 LLCs (this fourth LLC doesn't even need to be the owner of the other 3 LLCs). There are many companies that specialize in being the official employer of the employees of their client companies, for the purpose of centralizing payroll and other employee related formalities and services.
Which gives me an idea - maybe you want to look for a company like that (I know of one here in New York called Ambrose Employer Group) and have your problem resolved this way.