Technically, it's the "transmission control module"
Then there's the "body control module"
and then, etc., etc.
There's even a "module" that controls the fan speed....
and they're expensive (sorta)
If it's any consolation, and as you say the body is in great shape,
no rust, dents, etc., what the repair is gonna cost,
is far less than replacement cost of the whole vehicle.
In your location, you don't have to deal with snow, ice, salt,
so that car should last a long time.
BUT, repairs are necessary to keep it that way.
Any moving part, or electrical, is prone to 'going south' so to speak.
Balance your repair cost against new car, higher sales cost,
higher insurance, and all that, and expect that your next 'new'
car will be even more complicated in the control department.
Your mechanic should be able to locate a used 'module',
save you a few bux, but you (the wife) gotta expect repairs.
Just Common Sense......
err....I'm not a Doctor, but I'll take a LOOK ! !