Hi Jessica!
June is my favorite time to visit Walt Disney World Resort and I love that you are bringing the rest of the family along!
Disney After Hours is offered at three theme parks (
Magic Kingdom Park,
Disney's Hollywood Studios, and
Disney’s Animal Kingdom Theme Park), but they currently only have dates available until April.
Because you would like to plan something fun with your family, I would like to recommend a few alternatives:
H2O Glow Nights Pool Party at Typhoon Lagoon has dates available in June and takes place every Thursday and Saturday from 8:00 PM - 11:00 PM, but you can arrive as early as 6:00 PM.
How about a tour like
Behind the Seeds? It is a walking tour where you get behind the scenes look at The Land Pavilion. This is a unique learning opportunity if you are interested in gardening or natural sciences.
How about some family-friendly bowling at
Splitsville Luxury Lanes at Disney Springs. You can get a lane, have some good food and have a good time with your family.
I hope this helps. Please let us know if you have additional questions.
Have a magical gathering!
Raquel