Most if not all will be in our Disney photo books. So 5x7. Maybe slightly larger. My main concern is character pics and kid pics and good castle pictures and such..
If you're shooting in good light, almost any camera can handle that stuff. (including your phone).
I'd recommend the Canon gx7, the Sony RX100, as the top 2 choices. If you want to replace the D5100 with something smaller and better, I'd go with the A6000. (and you can get a few dollars selling the D5100 stuff).