I think it's reasonable that parents ask questions, want to see insurance, police checks, etc. It could just be that these parents having been told you are in the process of becoming licensed are waiting for that to happen as a means to valid the statements you made.
In all fairness, I think this is reasonable. We are strangers to them and while they have to of course just make a leap of faith to some extent initially until they get to know us, validating the statements made to them, is the only way of checking our honesty. Sure, they can take up references but for all they know, at the end of the phone is a personal friend pretending to have been a client.

What I will say, is that if your gut is telling you that these parents might be challenging, trust it. While as said, I think it's reasonable they are inquiring about the status of your license, they also have been told that you aren't in control of when that happens and done have a go date to give them.

For me, next time they ask, I would reply and say something like "I know you are anxious about the status of my license but like you, I too am just having to wait until the process goes through and the speed of that is subject to the work load the licensing department currently has. As you know, I can care for 2 (I think you said that?) children unlicensed and therefore if you need care to begin before the process is completed, that is an option as well.
The licensing department's number is XXX-XXX-XXXX should you wish to confirm that I am in the process of this before you sign a contract but please be aware that I cannot hold a space indefinitely for you without a contract and so if the licensing takes longer than we hope, there is a risk that you miss out on a space in my day care.
For now, that's all I can do while we wait for the process to complete. Of course, I will inform you of when my license is approved but between now and that happening, I have no other information I can give you."

If they still continue to message endlessly, then you can decide if your intuition about these potential client's still stands - you do not have to offer them a space. This is your home which just happens to be a business too. Ultimately, the decision is yours not the parents as to if they will come to you for care. Don't forget that. You are not obligated to take anyone's child just because you have a space open.