I don't know how far apart these two different places are. I would stay put and commute when the new daycare starts or wait a few weeks and put your child in. Moving is a total pita. It is didruptive to the family. It's not easy to find a place for just a few months. I'd do it only once given the choice.

You can find moving/storage companies to move your stuff to storage for whatever amount of time you need and then move it again to your new home when needed.

I think first off, I would not want to move 2 times! It's expensive to do, all you said, plus a major inconvenience. Maybe you could work out an agreement with your landlord to go beyond your lease until you move into the new home? As for your child starting "preK", see if you can start she/he in a program at your new location, it would just be late, or a "transfer" situation. I would try to do all this before I would move 2 more times!!
Good Luck!

They wont let me do a month to month - They want to put it on the market vacant.

I would probably ask to see if I could extend the lease until mid-September. Personnally, I would avoid a double move.

In Georgia, the landlord is required to give you 60 days notice in writing prior to the termination of the lease that there is to be no renewal. Cross your fingers that he forgets to do so.

Here is a link that might be useful: Georgia Landlord Tenant Handbook

Actually, verbal notice is sufficient if there's no written lease.