The other day, I was reading about Chris Terreri on here and it reminded me of him being traded by the Devils to the Islanders for John Vanbiesbrouck before the trade deadline in the 2000-01 season. Even though I don't remember the exact details, I remember reading in "Fish Sticks: The Fall and Rise of the New York Islanders" that he was disappointed and unhappy being sent to the Islanders. At least Terreri didn't have to move very far from New Jersey to Long Island.
It's funny to me, IslesFan, that as an Isles fan your first example is Chris Terreri. Because when I think of players "traded from a desirable/successful organization to the opposite" my first thought is another Islanders acquisition that was far, far more acrimonious: Kirk Muller.
Muller won the Stanley Cup with the Canadiens in 1993, and had been named their captain at the beginning of the abbreviated 1994-95 season, but at the '95 trade deadline was traded with Mathieu Schneider to the Islanders for Vladimir Malakhov and Pierre Turgeon.
Muller initially refused to report to the Islanders, so miffed about the trade. He absolutely did not want to be there. A few days later he reported and played out the rest of the season, and he did show up at the beginning of the next season, but he let it be known he wanted out the entire time, and by November of '95 Islanders management made the decision to just scratch him from the lineup and send him home. He was traded to the Maple Leafs in January of '96 as part of a three-way trade with the Senators.
Mathieu Schneider likewise didn't want to be there, nor did Wendel Clark, who was acquired at the beginning of the '95-'96 season in a three-way trade with the Devils and Avalanche (the Isles got Clark from the Avalanche, the Avalanche got Claude Lemieux from the Devils, and Devils got Steve Thomas from the Islanders).
Clark himself was basically in a double-whammy of back-to-back trades to organizations perceived as "lesser", going from being captain of the Maple Leafs to the Nordiques for Mats Sundin in 1994, then traded from the Nordiques/Avalanche just as they were getting good to the tire fire on Long Island.
Schneider and Clark were packaged together to join Kirk Muller in Toronto only a couple months after Muller's departure, for a package of young players (Kenny Jonsson, Darby Hendrickson) and the first-round draft pick used to select Roberto Luongo.