I've taken my backpack that I use for school before. The only thing to be aware of when wearing a backpack is where you are in space. People who aren't used to wearing backpacks tend to whack you with them, so just be aware of that.
I never had any problems taking my medium size student backpack anywhere. It can be taken on most attractions. I like to put my legs in between the straps to secure it on rides such as Rock 'n Roller Coaster and TofT. On RnRC, try to get a row in the front of the car. There's more space there. If you were to take it to Epcot, you might be better off on Soarin' letting them store it for you rather than trying to shove it underneath.
I don't like putting my phone in the backpack. I don't like having it out of reach. I have a small pouch that I wear over my shoulder and keep my phone in. As others have said, pouches in your backpack are essential.
Now let's get into alternatives...
I do prefer carrying a large purse with a zipper as opposed to a backpack. I went last January with a friend, and we took one backpack that had our wallets, jackets, and other stuff in there, and alternated carrying it. It worked well for us especially with the jackets. Normally, I just carry a large purse that fits drinks and other miscellaneous items. Just make sure that if you get a tote bag or something large that it zips.
The other thing that may work well, depending on how old your kids are, is to let them start carrying some of their own stuff around. Last August, I had my brother in MK with me, lugging all his drinks in a plastic bag and such, and felt like a packmule. So I bought him a cinch bag in MK and let him carry around his poncho, umbrella, and drinks. I carried around the expensive stuff like his iPod, but it was a much lighter load for me with him carrying it. And believe it or not, he loves having his own bag. Makes him feel grown up, I guess. A cinch bag can go on their backs so they won't just put it down and leave it someplace. I just make sure that when he does take it off that he puts it back on and that it's shut tightly. At bag checks, it's not really and issue as it opens easily, and I find in most cases that they don't look as carefully at bags that kids are carrying. So this could also be an option if you've got older kids.