I’d tell her you’re taking the car in for the “surprise starter”. Drive her to work, take her car.
Return with the Jeep and the Jeep Key. Throw some black electrical tape over the back of the Jeep emblem on the back of the key. (She won’t notice or care at that time.) Then ask her to come outside to try and start it. The rest will play out as one might expect.
Make sure you get this Jeep mod for the event.
[Also have some goof off to remove any residual adhesive if you do tape over the logo on her new key – but the electrical tape should come right off the plastic if it’s been on for only an hour or so]
Bonus points if you get a third person to film it from a slight distance.