While the rich saw their wealth accelerate greatly under the Clinton Administration, the poor made better gains under the Clinton Administration than under almost any other of the past several decades
Due to the aforementioned Dot Com bubble, which evaporated. And poor people used to be able to get into a low-skill industry that was nevertheless unionized and paid a living wage with decent benefits....not so much after NAFTA.
You're absolutely right that the unions lost ground under Clinton. However they lost less ground under Clinton than under Reagan, either Bush, or Obama.
The biggest shaft to unions was probably the passage of Taft-Hartley, done by Republicans, but that was waaay back in the 50's. Reagan fired a union that endorsed him, and Scott Walker has been a "wonderful" union-buster in Wisconsin. But nothing in modern history comes close to NAFTA - sure Republicans will try to undercut unions with right-to-be-fired laws, but NAFTA made unions obsolete in entire sectors of the economy. And even if the factories don't move to Mexico, NAFTA allowed employers to walk into a room and tell the union, "Yes, we have all time high profits, but you're going to take massive cuts to your pay and benefits, else this plant is moving to Mexico".
We've also had an overwhelming message of how terrible organized labor is (after all, who wants a 5 day work week, paid vacation, sick leave, or worker safety?)
The killer idea has been the notion that unions work to protect incompetent, lazy or criminal workers, which is nonsense as it's predicated on the idea that Bob is just dying to do his own work plus Steve's, if Steve starts slacking off and not doing his job. People simply are not built that way, unless it's in an abusive Biff Tannen/George McFly situation, which can just as easily happen at a non-union shop.