Can keep my header when widening a doorway?
Not if you want it done right, but it's not as bad as you might think. Here's my usual routine to avoid excess drywall repair. 


Remove the current door and jamb.  
Mark the new rough opening on the wall.  
Make the horizontal cuts to widen the rough opening using a circular saw (which will be extremely dusty--have a helper hold a strong vacuum) and/or a reciprocating saw. At this point the current header is still in place, but you've cut through all studs interfering with the new rough opening.  
Make the vertical cuts on each side. With luck you'll be between studs. If not, just cut the drywall for now. Remove all drywall inside the R.O. on both sides of the wall.  
Remove any studs at the sides of the R.O. that are within 1-1/2" of the R.O. You may need to remove drywall screws and extend the horizontal cut slightly. You should now have voids between drywall panels, at each side of the R.O., of at least 1-1/2" depth into the wall cavity. At this point you may want to stand your new door in the opening to be sure you have the R.O. correct. You want about 1/2" gap all around. 
Remove any drywall screws run into the header. Gently pry the drywall away from the header to locate them. A magnet can help. Once the drywall is completely free, pull down the header. It'll probably be toenailed into the pin studs above and may take substantial force to dislodge. Once it's out of the way, reach up inside the wall cavity and pry out those nails. You could also cut them off with a rotary tool. The bottoms of the pin studs should be free of obstruction.  
If necessary due to a taller replacement header, mark the top of the new header above the rough opening. Make surgical cuts with a reciprocating saw to shorten the pin studs appropriately. If you're very careful, this can be done by cutting through the drywall on one side only. It's easy to let the saw jerk the studs around and rip up your drywall here. Go easy. You'll have to repair these small slots later anyway, so you can add extra drywall screws to better anchor the pin studs if you like. Remove any drywall screws and the pin stud cutoffs. 
Add new king studs where needed. Anchor them in place however you can, by toenailing into the wall plates and with drywall screws. If you have an existing stud less than 6 inches from one side of the R.O. consider extending your header to use that as a king. It's important that both kings be well anchored at the top and bottom, as they're critical to a rigid wall and robust frame for your door. If you can't get nails or screws in place, use a copious amount of construction adhesive (not wood glue). 
Slide the new header up into the wall cavity. It might hang there of its own accord, but you could run a couple drywall screws in to temporarily support it, or place a 2x4 leg under it. Toenail or screw the header into the king studs. 
Add your trimmer studs. If you used a king that's more than 3" into the wall, add double trimmers on that side, flush with the R.O. You'll want 3" of lumber there for rigidity and for trim backing. Fasten the trimmers to the header and re-fasten the drywall to the trimmers.  
Repair the slots and any screw holes in the drywall above the header as necessary.