Since you haven't been in 30 years many things have changed and there more parks, resorts and restaurants. Unfortunately to many of our here dismay the night time parade is no longer. It sounds like you are commited to Magic Kingdom. As I mentioned many of the rides are doable unless someone in your party has mobility issues getting in and out of the ride vehicle. For example Small world as a boat ride has low seats and you have to step "down" into the boat. My parents were able to get in/out with me holding a hand and help get in and out and using the back rest of the bench in front of you.
Rides at Magic Kingdom
Pirates, boat ride same loading as Small World
Aladin Spinner: Easy in and out but if someone has problems with dizziness or motion sickness may be an issue
Haunter mansion Easy in and out HOWEVER is a moving people mover to get in/out, may be an issue if you have balance issues or use cane etc. Again my parents were able to do this in their 80's with minimal assistance.
Hall of Presidents: Show no problems
Small Worldas described
Peter Pan: Same loading/unloading as Haunterd Mansion.
Mickey's Philharmagic A Show, no problems with in/out.
Pooh, same as Peter Pan Easy in/out however does have a people mover.
Dumbo, Spinner like Aladin
Tomorrow Land Transit Aurthority Elevated ride thru tomorrowland, has a people mover to enter the vehicle, same as described for Haunted Mansion
Laugh Floor, Show no problems.
Buzz light year, arcade stly ride: Same in/out as MAnsion with the people mover.
So as long as you party is able to navigate getting in out of a ride vehicle from a slow moving people mover most these are all very doable.
What day to pick? Try to stay away from days when there are extra magic hours for resort guests. Stay away from the weekends if you can and the friday and monady of MLK weekend.
Something to consider would be doing the special ticket event of Night time magic. T
hey say it start at 7pm but I believe and would have to confirm they will let you in at 4pm. If so you could plan to enter at according to Tullavu it statrts at 7pm do the attractions that are not running during Night Time magic that your intereseted in, watch the fireworks and then have the park with much lower crowds. The drawback is if the weather sucks, your stuck.
Here is the link to look at this:
Add even more magic to your visit with this unique experience at Walt Disney World.
disneyworld.disney.go.com
Just looking at the dates this is available, January 23 looks like a good choice. You could plan on doing a nice lunch at one of the monorail resorts and then take the monorail to the Magic Kingdom. The other advantage would be that you could park at one of these resorts.
Parking at any of the parks: There is handicap parking, however where ever you park you have
a short walk to to the tram that takes you to the entrance. At MAgic you will have to take the monorail or Ferry to the entrance.
Are you Florida Residents? I know you said you are only looking at one day but I have to through this into the mix lol. The have a special 3 day ticket.
disneyworld.disney.go.com
It would really give you the opprtunity to see all the parks at a very nice pace. Your party would love Epcot and Animal Kingdom. Please really consider it. I think you may kick yourselves if you only go one day to magic kingdom. Really my parents have travelled all over the world and in their old age they enjoy Disneyworld the most because it so handicapped friendly and can be very laid back if you have the time.
Sorry if this post if overwehlming , like you are planning the D day invasion, but there are many of us here that can help you through it.