Hello Brian,
Thank you for coming to us with your important questions. All of us here at the Disney Moms Panel want to help other guests as much as we can so that you are prepared for your Walt Disney World vacation.
While I can understand the convenience of a wagon for your four children, unfortunately, wagons are among the items prohibited from the theme parks according to the
Park Rules and Regulations. If your strollers are too cumbersome to pack or maneuver,
strollers can be rented in each of the theme parks. Double and single strollers are available on a daily or length of stay basis. There are also several independent stroller companies that rent and deliver to the Walt Disney World Resort hotels so that you can have access to strollers outside of the parks.
In regards to looking for dining reservations based on recent cancellations, I would recommend you keep trying each day leading up to your vacation. It is impossible to know exactly when someone is going to cancel. However, many guests will cancel their reservations about 2 days prior so that they do not incur a cancellation fee. I hope this helps you acquire those reservations you are hoping for.
Have a magical vacation with your kiddos. It is sure to be full of memories to last a lifetime.
~Allison L