I've fix dozens laptops with power jack problem, never been so hard. most time, you don't even need replace that jack. re-solder it is more than enough.
for removal, Clean it up a little bit, 40W sodering gun with 350 C degree with desoldering tool, or just power desodering gun, will works fine. if u can't melt solder on MB. put a little rosin core 63/37 solder on, it'll will greatly lower the melt temp for those Pb free solder. MB is multi-layer board, heat transfer is much faster than single/double layer board. U need more patiant not tig welder to do soldering and de-soldering.