Problems with front derailleur shifting on an inexpensive bike
I'm sure you're a better judge of how effective your LBS employees are than people on an Internet forum, but in my experience it isn't uncommon to find some LBS employees are not very enthusiastic about working on bikes they view unfavorably for whatever reason: too old, too inexpensive, and so forth. Some think that working on an inexpensive bike is like polishing a turd, and I have run into more than a few who view it that way.

If the bicycle is similar to this one, I would encourage you to check out some YouTube videos regarding derailleur tuning:

Tuning a front derailleur
Tuning a rear derailleur