I’ve been playing Outwitters nonstop for about a week now. It’s turn by turn strategy where each player controls a team of beasties in an attempt to get to and destroy the other base. You can play with your wife taking turns on the same iPad or each using your own. It’s also got a really robust league system so you can play strangers and it will automatically match you with people of roughly your skill level.
There are three factions you can play with, each of which has seven units. Six of them are functionally the same, with the special unit varying from team to team in what it can do. The game comes free with one team, and that’s all you need to play forever, but you can buy additional teams. They’re cheap – currently $3 for the whole schmear.