Joined: Feb 2012
Posts: 19,351
Likes: 5,467
From: Rochester, NY
Bikes: Stewart S&S coupled sport tourer, Stewart Sunday light, Stewart Commuting, Stewart Touring, Co Motion Tandem, Stewart 3-Spd, Stewart Track, Fuji Finest, Mongoose Tomac ATB, GT Bravado ATB, JCP Folder, Stewart 650B ATB
Generally only the left side uses plastic retaining cups. One trick to reduce their breakage possibility is to loosen the right/drive side first. This reduces the force needed to remove the plastic cup.
BTW "Before using more force, do you confirm 1) it's the right tool, and 2) it's the usual threading on both sides (lefty loosey)?" could be miss understood by some. My answers might be yes, do confirm the tool and threading before using the tool. Andy (fighting the trend to minimize verbiage which also increases ambiguity)
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AndrewRStewart