Accidentally deleted info from game center

Hi all. On my wife's iPad 2 she plays the game My Town 2 and recently was having some trouble with it. I told her to go ahead and delete it, then reinstall it. Upon doing so, when asked if you wanted to keep or remove the info from Game Center, "remove" was accidently hit. So now after reinstalling it, the game is starting over from the very beginning instead of picking up where she left off. I do have the game on my iPhone, and it is at the point in the game where she was. Is there a way I can get the info on my Game Center for this game back onto her iPad? We are both on the same iCloud account, and I've heard you can use this to sync game data, however I'm unsure of which options to have selected in iCloud to make this happen (if it's even possible). Any information would be greatly appreciated! Thank you!