No precision approach into SOU, so would have been a VOR/DME. When crew go visual, by MDA, if not positioned well for a landing, two options: reposition if safe to do so, or if too far out of position it is a go-around and try again. MDA at SOU escapes me, but I think it is around 700ft. Also the FAT on each runway is offset from the c/l in the order of 8 to 12 degrees depending on the runway - one end is more offset than t'other - hence the manouvering to align with rwy c/l. Not dodgy, perfectly routine, and would be performed by any airline using an approach offset from the c/l. However, the more precise the tracking, the less manouvering required!
There are limits to the amount of attempts to start an engine, so a pull back onto stand sounds sensible, to sort the problem. Vibration on takeoff can occur - excess vibration is easily spotted on the engine vibration indicators. If it was general wobbiliness(?) a stiff crosswind can mean a little wobble after rotation as the pf arranges the controls and attempts to follow the sid! Obviously the more experienced the pf the less the wobbles!
Finally are you sure it was the engineer who jumped on the a/c after landing at SOU, or just a very eager dispatcher trying to get the maybe late aircraft turned around and back out again?
Commercial operations are very different to pa28 ops - as I'm finding out, but I'm sure that at no point anybody was in danger! I'm sure that safety in BACON would be taken just as seriously as anywhere else in the industry, unfortunately, with much respect, as a ppl a little knowledge can be dangerous with respect to conclusion jumping.
Aircraft will always go tech, and other glitches such as an a/c blocking another on stand will always happen irrespective of airline. Just unfortunate they happened to you in quick succession.