I am exactly like your wife & always worry about being underdressed. We went there for dinner last year and I made us go back to the room to put nicer clothes on and as soon as we got there my husband quickly pointed out to me there was a mix of people dressed straight from the parks to fancy.
Noone will notice what you are, or aren't, wearing so just go and have a fabulous time!!! Logically, I know this, but can't seem to tell myself that : )