Engine runs poorly when cold

First of if you have a bad instinct about the service repair shop you are going to, you should go somewhere else. Thissite has helpful links to help you find reputable shops near you, just do a search.
When looking for a shop, look for the shop to be clean, personel to be proffesional and diagnostic equipemnt and overall appearance of shop to be up to date.

As far as the engine problem, you might want to check the fuel pressure first. That is something you want to elimate from the start. Otherwise the Idle Air control Valve, IACV, may be at fault or if so eqipped, the Fast Idle Thermo, FIT, may be failing. Both control idle mixture and/or idle speed and are controolled by angine load and coolant temperature. So, they act as a choke that is sensitive to the engine warming up and will also adjust as needed to going up a hill or if you turn on any accessories.

The other thinig to do is to have the trouble codes pulled. This will help to track down the source of the issue. There is a On Board Diagnostic sytem that can be checked for failed parts. Sometimes auto parts stores will check them or a repair shop should not charge mush to do so.