Would it be possible for you to leave the kids with your parents, drive to WDW, check in and leave luggage, then pick up the kids and return the car?
I thought that was a decent idea.
With that many resort changes, you might want to consider keeping the rental car for the whole trip. I've done split stays where we've used Disney to transfer our bags and where we've thrown the bags in our rental car. Both work fine, but if Disney transfers your bags, you likely won't see them at your new resort until very late in the day. That's an added cost, but sometimes the longer term rental ends up being less expensive than a short term rental. I know this wasn't your original question, but I just thought I'd throw this thought into the mix.
Oh, most definitely.
27-June 30 at my parent's house. June 30-July 2 at AoA. July 2-July 3 BWV. July 3-July 4 BLT. July 4-July 7 BWV
No chance of doing SSR or OKW for the trip and just staying put?
I finally out-split-stayed myself on our last trip, with POR 1 night, then 3 night cruise, then Kidani 3 nights, SSR 3 nights, and VWL 2 or 3 nights (not remembering right now). That was pretty bad, especially b/c we had to switch after one night at SSR b/c of problems with the room.
Yours has even shorter stays once you hit WDW.
A car would make those moves MUCH easier.
If you do really want to stick with those plans, for the BLT night I would really recommend you do a switch of packing, get everything for the 3rd and 4th into ONE bag and check the others at BWV as you're leaving. That way you aren't moving everything else along, and can just be focused packing-wise.
I don't think I'm an overpacker, since I think about everything I am packing and use everything most of the time (the things I don't end up using are light or small, it seems), but to others it would definitely appear as though we just shoved everything in our house into bags...I definitely know what it's like to be carting large numbers of bags from place to place, and it's not much fun, even when you know what's in the bags and know what you'll be using everything for. So for the times when you can, I'd stash extra bags and streamline one of the shortest stays.