You'll need a rental car in Tunica, and there's absolutely nothing for the wife and toddler to do there. You can still find decent games in Tunica, but with those restrictions I'd recommend Biloxi instead.
In Biloxi, the best games are at Treasure Bay (although this can change from week to week) and for higher limits Beau Rivage. I'm no help on package pricing anywhere. FWIW, I wouldn't choose T Bay to stay, as they are the bottom rung on the ladder for accomodations. Reasonable alternatives are Beau, IP or Isle of Capri.