Having trouble syncing an App

I am trying to sync an app to my daughter's iphone 3GS.
I have tried numerous things.
It is checked in itunes to sync apps, and this specific app is also checked.
I have tried deleting the app and reinstalling it. I have also tried to reboot the computer and the iphone.
The app shows up in itunes, and i have dragged and dropped it onto one of the pages of the apps in the sync apps tab. Then I hit sync. But it does not show up on the phone. Twice, the icon showed up and said it was installing, but as soon as the status bar was filled, the icon disappeared.
I have tried to go to the app store right on the phone, but it says it is installed already.
I even tried searching for it in case it was somewhere that I was missing.
I'm not sure what else to try.
Any ideas?
My daughter is dying for this game lol

 

I tried that, as I said above. It says its installed already.

When I gave her the phone, we made her a new itunes account...its possibl theres some mixup with the separate accounts...I've logged back into my original account (since it was my phone first) and we are still having the same problem...and 2 other apps are doing the same thing now as well.

What about removing the sim card and/or resetting the phone back to its original settings?

 

Resetting it to factory didnt help either.