I like your idea of training. Make sure they wear shoes that they'll wear on vacation, and rotate among all the shoes that they'll use.
I seem to remember guidelines from my scouting leadership days that said children 10 and younger should not be taken on "strenuous" hikes of more than about 1 1/2 miles. Ages 11 and up can ramp up to about 5 miles, more for older children.
Now, sure, on vacation at WDW, they're going to walk a lot more than that (maybe), like 6-8 miles as another poster said. But some of it is more like "strolling" than the walking you do on a treadmill, plus, you take frequent breaks to stand in lines, do/see attractions, shop, eat, etc.
On the other hand, the treadmill is not "strenuous" like hiking on a rugged path through the woods with varying elevation either.
For DAILY training at their ages, especially for the younger ones, I would limit training to about 1 1/2 miles/day. You might want to have them do more on limited occasions, like up to 3 miles once a week, but I wouldn't go more than that. You don't want to overstress their bodies (imaging bringing a 5yo to WDW with a strained achilles tendon, for example - to say nothing about how awful you'd feel if they hurt themselves training), and you don't want them to be exhausted the first day of vacation. And make sure you talk to them about striking a balance being agressive with training, but knowing when to stop if you think you are overdoing it.
Also, why not have family walks OUTSIDE and enjoy the outdoors together rather than do the treadmill every day? That would be a nice change! I know there are practical considerations, like who has the time, for example (I know very well how that goes - I have two kids myself) but I think walking outside doing various different circuits is much less boring than treadmill everyday. And it will give you something you can do together as a family!
Have a magical trip when you do go!
