I need your help!

The very young kids and babies will definitely need rest breaks, which means the parents will have to take them also. The 60-somethings might need rest breaks, but they might be able to go all day long - it depends on their fitness level and ability to tolerate the Florida heat. The teens almost surely will have the energy to go all day, even in the July heat. And both the 60-somethings and the teens may or may not be willing/able to take a shift or two watching the little ones so the parents can have a break.

Trying to force everyone to follow the same schedule (no doubt dictated by the needs of the youngest kids/babies) could result in a lot of aggravation and disappointment on the part of the 60-somethings and most especially the teenagers. So the one piece of advice I would offer is to get at least two rental cars and not to be wary of splitting up during the day. With such a large group, they'll either need two (or more) cars or one really huge van, and the cars might actually be more economical. But even if they go with one huge vehicle, I'd suggest they be willing to leave the teens and maybe the 60-somethings behind at the park of the day while the parents take the young'uns back to the villa for a rest break, and then meet up again in the evening.

It's a pity they aren't staying on-site since Disney transportation would take care of the problem.

Not wishing to offend, but we have found going with large groups no matter the age, can be slower and less done. It might be a tip to suggest they break up the group into smaller ones and then they can break as they need or run as they want. Then they set up meeting points where they can all sit down for a meal or a show.

Just a thought

My DH and I eat off site quite often. There are many reasonably priced restaurants between WDW and the Universal/Sea World area. Many of these restaurants offer free kids meals w/ the purchase of an adult meal. Many also have email clubs you can join and get free appetizers or meals for joining. The email clubs almost always give a free meal on your birthday as well.
Here are just a few examples:
Fuddruckers- Join the email club and receive a free or discounted meal on b-day and anniversary of joining the club.

IHOP-kids eat free promotion. They usually have at least one day a week(sometimes every day of the week) that kids eat free w/ the purchase of one meal per adult meal, 4pm-(hours vary) They also have an email club that gives you a free meal when you join, on your birthday and on the anniversary date you join.

Benihana-register for their email club, the chefs table, and receive a $30 gift certificate during the month of your birthday.

Maggianos little Italy-join email club and get $10 for signing up and $10 on birthday

There are many more restaurants that offer free apps or dessert. Plus many that send BOGO coupons in my email quite often(Ruby Tuesdays and Longhorn Steakhouse for example)

If they sign up for enough email clubs, at least one person per meal could eat free. My DH and I only ever pay for one entree when we go out to eat because I've joined so many email clubs

Those with the babies will definately want to use the Baby Care Centres within each Disney World park..
They are a godsend for parents to change and feed their child..
It's also great places to get out of the heat for a while.

As most people have said - There will be tension between the age groups.

I would say there's nothing stopping you going to the same park, but split up and meet for meals or fireworks or shows.

indeed, there's nothing stopping the teens hopping out to another park (If you can trust them!)

If you are staying off site, check to see if the place you are staying offers free kids meals. It saved us a bundle years ago to feed free breakfast and dinner for the boys.
But if people want to go back for a break, everyone can eat lunch and those that need or want a nap/pool break, etc can do so.