i had same problem. 109,000 miles, 2008 tucson, check engine light came on, autozone showed oil control valve bad, bought part for $119 (amazon had it for about $67 but i couldnt wait). viewed YouTube for instructions. one 10mm socket removed bolt.
aaaannnd stuck. it would not budge. twisted with plyers and the end broke off. tapped with hammer and screwdriver and twisted with plyers. nothing. no love.
went back to autozone and with help they recommended nano penetrating oil and a 9/16 extractor ($7.00 more) or worst case, remove valve cover and tap it out from the inside, yeech!
so i sprayed the penetrating oil, waited a few minutes then inserted the extractor and twisted.
magic! the valve became unstuck and i sprayed more and twisted more.
a couple minutes of this and it slid right out! the new one slipped right in. easier than a spark plug.
the local repair shop wanted $410 to do this job. plus an additional $100 to put the car on their scanner.