I'm not one for playing mechanic in a parking lot so bare with me.
Yep, wife's car and she's going to call you and you have to decide if the car comes home (always my choice) or she continues on with it. I don't know about your wife, but having been married a couple times now, I'd bet that there would be the "yea, but is it going to start later?" conversation that you probably won't win. In other words, you'll be driving her Fury while she drives off in your vehicle.
That said, I've been driving these cars and owned a ton of them back when they were worn out used cars. Many thousands of miles in all weather. Like ballast resistors, I think I've had two starter relays go bad... and they were in cars that were bought for less than $300 and my time with them was just before they were scrapped. I've lost a lot more starters. So there's other parts I'd carry first... But really a AAA card might be the best thing.
If you want to carry one, go for it... I'm just giving some advice based on my experiences.