Hi Billie,
One of the wonderful ways Disney supports families is by having
Baby Care Centers located at each of its parks. Here parents can nurse, change and take care of their little ones needs. They also have a small supply of baby essentials, microwaves, sinks and television.
At Magic Kingdom, the Baby Care Center is located off Main Street between Casey's Corner and the Crystal Palace. At Epcot, the center is located in the building between Test Track and Mexico. At Animal Kingdom, it is located with First Aid by Creature Comfort and is located at the front of the park at Disney's Hollywood Studios.
Parking is free for guests staying at the Walt Disney World Resorts. Save your receipt if you go to another park you only pay once a day.
As for places to get engaged, in Epcot, if your intended has a favorite country, that would be the spot. If not, the Eiffel Tower in France would be a good choice. A little bit more private could be by the koi ponds in Japan or on the ride in Mexico.
In Animal Kingdom, I would choose the bridge walking towards Kilimanjaro Safaris. Or the path that heads from the safari to Everest would be a great spot as it has the Tree of Life in the background and that seems symbolic of a starting a new life together.
Wishing you a magical vacation!
Beth