Yea this whole LBS situation sounds kinda iffy. Even if they can't replicate it, they can suggest/try some things. And as for the gear skipping, they should be able to fix it (whether that fix requires replacing something or not is another question).
As for riding/sliding, your tires seem pretty big as is, I would look for something with more aggressive treads if you plan to do anything other than smooth road. I can ride my cross bike with treaded 32's on the road, I cant really ride my road bike with 23's on gravel, however
If the roads in your area suck, try taking the bike somewhere else (in your car) until you get used to things and more confident.
As the saying goes 'When you fall off the horse-bike, you have to get back on'....or something like that