Don't worry. We have a cottage about 1 mile from the area you are staying in and we'll be there around the same time with 2 11-year olds and we can't wait to get there. As for construction, there is quite a bit of construction going on along 30A including in your area, but you could ask your agent/person you rented from if it is within earshot of where you are staying and if any construction is blocking the path to the beach (which I doubt very much since the beach paths are the communities' bread and butter). I've driven by the area you'll be staying in and it is very nice. I believe you're staying in the community with the huge pool. You'll face some construction on the road (30A) between where you're staying when you go west toward Seaside or Grayton beach (because a new upscale community is being built called Alys beach), but that hasn't bothered me and I haven't seen any traffic bottlenecks nor have I heard any of the construction at all -- you're in an area of 30A that doesn't have a lot of traffic anyway. The construction near Alys beach has blocked off the bike path for a little while so you'd have to take your bikes on the road for a short way if you ride bikes or run. Frankly, it has been irrelevant to me when I'm there.
The beaches did get a hit from Arlene so the sand may not be as white as it is most of the time (although it may be back to normal by the time you get there), but it's still a lovely beach and the sunsets which are amazing and emerald green water aren't affected at all. People who love the beach realize that Mother Nature does her thing and the beach changes regularly -- that, in fact, is the beauty of it.
As for what we'll do when we get there, we'll hang around the pool and the kids will look for frogs in the mornings as soon as they get up (they take a bucket and catch them and then let them go after they've named them), we'll go to the beach in the mornings while it's a little cooler, we'll go to the beach and watch the sunsets every night (sometimes with a picnic dinner), we'll go to Grayton Beach state park which is amazing and has bathrooms and showers and picnic tables and grills and costs about $5.00/car for entrance fee, we'll go to Angelina's for lunch at least one day during the week for an inexpensive and good lunch (although we'll go there early because it will be very crowded in July), we'll go to to the dollar store in Panama City Beach (there are lots of them) so the kids can entertain themselves and shop for just a few dollars (I'll bring a book to read while they are shopping), we'll get a puzzle started and work on it off and on throughout the week, we'll play a few games, we'll watch a few movies, we'll go to shell island on the ferry at low tide to look for shells (which we've never done before but this will be our big experiment this trip), we'll check out a few other public beaches that have bathrooms (which makes it easier for kids), and I'm sure we'll do lots of other things as well.
If I could be there now, I'd be there in a second... We're going in July and again in August. We also go in November (lovely because it's when the monarch butterflies pass through the area on their way south and they're all over the paths to the beach), New Years, at least once more in the winter and at least once more in the spring. We can't get there enough -- regardless of construction or changes in the beach. The area is really very special.
So, call your agency or whoever you rented from and ask them directly about where the nearest construction is to where you're staying and if any construction is blocking the beach access. Then relax and enjoy the trip.