Where I live it's an hour and a half truck ride to a bike mechanic. Luckily this forced me to learn how to properly maintain or repair all my bikes. I think your wife's bike is either shifting improperly because of a bad component or adjustment, or she is having operator issues. You may be very happy with the shifting once these are addressed and an upgrade in parts won't address either issue anyway.

If your current mechanic can't get that drivetrain working, I wouldn't want him to install an upgrade and expect it to work better. Your best option is to learn the basics of adjustment from Park Tool vids on youtube and see if you can get the shifting sorted out yourself. All bikes will occasionally require adjustment or replacement of parts. You don't want to have to run to the bike shop for something as simple as a cable slipped or stretched and you need a tension adjustment on it to make it work. You need to learn all the basic things anyway.

When you know her bike is operating perfectly, then you can decide why something different would help her. You could learn that she would prefer something completely different to fit her riding style. She may prefer an internal geared hub and the way it shifts to any derailure system. She may like a 1X system.