Some combination of these two things ought to do. You should be able to acquire both at a total cost of less that 30 bucks.

http://www.parktool.com/product/cran...acket-wrench-1

http://www.parktool.com/product/cran...bracket-wrench

As for one side being mega stuck in, thats supposed to be that way (although your reference to LH side is confusing me since most adjustable BBs I have had have the fixed -- aka "mega stuck" -- cup on the RH--i.e. drive -- side, but perhaps some are reversed as would appear to be case if picture you show is oriented correctly). One side of BB has a fixed cup (the cup with the wrench flats on two sides) and is designed to be tight. The opposite side, with the notched lock ring, is the adjustable side. When BB adjustments are required, you use hook spanner wrench to loosen the lock ring, then the pin spanner to turn the actual cup, which is only tight enough to remove play but not tightened so much that the balls cant move freely. Unless completely dismantling the bike, you leave fixed cup in place and service bearings from the opposite side after you remove lockring, adjustable cup, and spindle. You just extract the bearings from the fixed cup side by pulling through the BB shell from the opposite side.