[Christ]

Make sure your key is on before you leave the clutch out to restart the engine, otherwise you'll throw a CEL in some cases, when you finally do turn the key.

If you're stuttering on restarts, then you need to be either a little easier with the clutch pedal, or a whole lot more liberal with it. It's either all at once, or a little at a time - there is no middle ground. I prefer the all at once method most of the time, but I don't mind the clutch shock - I have solid motor mounts.

What's probably happening is referred to as clutch chatter... you're letting it slip too much while applying torque, and it's "jumping" around on the pressure plate/flywheel mating surfaces.

This all assumes that your car used to work normally as well - some vehicles are equipped with security systems that don't allow them to be clutch or torque-started at speeds higher than X MPH.

Try this - While you're driving, hit 50mph, don't take it out of gear, and shut the engine off for a second. Turn the key back on, and give it some gas... does it stutter? If it doesn't, then you just need to adjust your clutch technique. If it does, you might try adjusting your key-on timing before you restart your engine using the clutch, or you might also try just starting it w/ the key instead of pop-starting it.