1) Sleep in and have a leisurely morning...
...depending on where you're staying, order room service and enjoy breakfast on your balcony or grab coffee and pastries and stroll the grounds of your resort.
2) Head out later in the day, when the crowds thin out (BONUS!) When 3:30 hits and the kids start melting down all around you (not to mention the adults!), go get your favorite beverages and relax on a bench.

Enjoy the evening EMHs and fireworks.
3) Try and snag a late dinner ADR at someplace where there usually aren't a lot of kids (California Grille, Citricos, Jiko....) - not always impossible to snag a same day ADR if you don't mind eating late. If you really time it right, try Calif Grille around Fireworks time - even just for a cocktail in the lounge - and go out on the observation deck to watch. Soooooo romantic.
Ooh... one more suggestion...
Do a dinner or lounge monorail tour:
Lounge - have a drink/appetizer in a lounge in each of the resorts on the monorail
Dinner - have drinks/appetizer at one, entrees at another, and dessert at 3rd
Oh! And go on all those crazy kid attractions, scream, yell, giggle and BE the kids for a change!
Congrats and have a wonderful time!!
