Plan for frequent stops and be careful of the weather, especially heat. Rather than planning on distance you can travel, you may have to consider how many hours a day you can bike with them being so young. Whatever you can do to keep the kids comfy and happy will be the order of the day .

Chariot has a sling, the Weber is not sold stateside that I have seen, so not much info here.

Good luck, post a blog and pix of the trip!