first off, there is never any reason to pull the parking brake when you are moving. its why its called a parking brake and not an emergency brake anymore.
second. i would first check to see if your brake pads are worn, not much point in adjusting anything if the brakes are shot.
my guess would be the calipers are out of adjustment. easy to fix. there is a 14mm nut on the back of the caliper, undo that and there is an allen head bolt (4mm i believe) underneath it that adjusts the piston in an out. the 14mm bolt is essentially a protective cap. tighten the allen key all the way until it stops, then back it off at least a half turn. this will ensure that the piston is nice and close and when you pull the parking brake handle it engages quicker.
don't bother adjusting anything from inside the car. there is an automatic adjustment system that usually keeps the cables adjusted properly, but if your pads are worn way down, the way i just oulined for you should work pretty good.