Suppose they agree that Alan will open curtains 1 or 2. If he finds the car the game continues, he is removed and Becky comes out. If he doesn't find the car the game ends before Becky comes out. So at that point she knows the car was behind 1 or 2 with probability = 1/2 that it is behind either one, and probability = 0 that it is behind curtain 3.
I think this means that from her point of view the keys are behind 3 with P = 1/2 and are behind 1 or 2 with P = 1/2. So her strategy should be to open curtain 3 and then either 1 or 2 and find the keys with probability = 3/4.
So overall strategy has prob= 2/3 x 3/4 = 1/2 of winning.
Hard to believe that the Ask Marilyn version of the Monty Hall problem appeared in 1990, 30 years ago, and the original MH problem dates back to the mid-70s I think.