If your wife shows up and doesn't take the rental, you could very well be on the hook for the full non-discounted price of the rental plus a no-show fee. Way too risky in my opinion.
I think you're left with two choices here: 1) Cancel it now and just go with the Alamo booking, 2) Call Avis and explain the situation and find out what their round trip rate would be, then decide whether to go with it or cancel it.