Hi Sally,
As you know, Extra Magic Hours is a perk provided to guests staying at a Walt Disney World-owned resort.
If the park "officially" closes at 7:00 p.m. and will be hosting
Extra Magic Hours from 7:00-10:00 PM, then starting at 7:00 PM guests will be asked to show their Resort ID in order to access shows and attractions. Every guest age 3 and over must have Resort ID. Of course, parents can hold onto the ID for their kids and just show it to the Cast Member at the attraction's entrance.
Guests without Resort ID may certainly stay in the park to eat, shop and soak up the atmosphere.
To avoid any misunderstanding with children wanting to ride Dumbo one more time, I would suggest heading for the exit around 7:00 PM. Feel free to linger in an area away from attractions such as Main Street USA where you could stop for an ice cream or other treat on the way out of the resort.
I hope this information helps your family plan accordingly. Have a wonderful vacation!