Can we take our wagon for grandma/pa's folding chairs and all the stuff a family would need for the day?

Yes, you can take it. No food is allowed in the park, but you are allowed to go out and back in.

We arrived mid morning and left for food and a break..regrouped and returned had a wonderful rest of the day and Roxannes advice above is spot on.

Yes. You can also take a ice chest full of water and ice only. We buy stuff for sandwiches and take a lunch break outside on the lawn and head back in.