First off, I would check with the boys re the baseball. My DS16 would be very upset if he had to miss the beginning of baseball practice (as would his coaches) and it could have a negative effect on his season. Our last family Disney trip was over Christmas vacation last year because it was literally the only time when nobody had an activity we had to work around.
My boys were 19 and 15 on our last trip (DD was 11).
Food - eating is, hands down, their favorite thing to do at WDW; buffets and family style meals were especially popular and they ate a frightening amount of food; they don't mind character meals at all, as long as they can eat, they are happy. We went to Crystal Palace (DD's request) and they were great. Some of their favorites: 'Ohana, Biergarten, Hoop Dee Doo ( I HIGHLY recommend this with teens; they will actually laugh/ smile!)
Photos- If you get the photopass or whatever it is called these days, you will get all the ride photos. This was a great perk with kids that love to ride the big rides. Even if you don't stop for many extra pictures, you may end up with more photos then you think just from the ride photos.
Touring - We generally stick together, but have no problems splitting up if the need arises. Teens like to sleep, but mine are full aware of the benefits of rope drop. So, they do get up willingly for rope drop/ EMH etc.. but we usually schedule in a couple sleep in days as well. On those days we like to take advantage of parks that have later hours. If you do decide to split up, just remember that the 13 year old isn't old enough to enter the parks alone. Otherwise, there are no restrictions for your group.
Magic Bands - decide if you want your teens to have charging privileges and be clear about what they can use the bands for. (They will need to know the pin #) My kids were allowed to charge back to the room/ access our dining plan and this was great as they could get their own food etc... without an adult.
Fun for you: If you can manage it, I recommend some princess meet 'n' greets. The princesses can be very funny with teenaged boys. Drizella tried to steal DS16 for her own, Ariel wouldn't take the photo until he was sitting right next to her, Merida was quite indignant with him wanting to know if he was trying to marry her etc... lots of funny moments. Actually, most meets with teenaged boys can be a lot of fun if you can convince them to try it.
Just curious, what resort have you booked? My boys definitely will stay anywhere, but definitely have their favorites. Favorite value: Sports; Moderate: Coronado Springs; Deluxe: Animal Kingdom Lodge
At the bottom of their list: Port Orleans French Quarter and Grand Floridian
Let me know if you have any specific questions.
