I will definitely fly if I were you. Sunset Limited east bound trains are notorious for their lengthy delay. You are very likely to have to spend a cold night in New Orleans with your two year old daughter at the union station and maybe arrive in Orlando in the middle of the night. You trip back should be slightly better but again you may miss train 58 to Chicago due to relatively short layover.

You may enjoy the train ride but I really don't think your daughter will.

By the way, if you really want to take the train, plan one night stay at New Orleans would make your whole trip much enjoyable. But I guess this would cut your vacation very very short.