2002 Honda Civic LX, 129K miles. Had brakes serviced at a local garage about 3 years ago. Have never felt or sounded right afterwards. Vibration when pressing down on brake pedal and it squeaks when released. Took it back to garage and the mechanic said if I wasn't happy to take it to a Honda garage - he did what he could and couldn't do any more. Honda refused to work on it when informed I had the car serviced at non-Honda repair center. Brakes do work, but the vibe and squeaking problem getting worse. What is the likely cause and what is my best option at this point?

 

just grab some white lithium grease and shoot it lightly on any moving part down there

 

It sounds like you are getting jerked around by a couple of grease monkeys! :-) I also have an '02 Civic LX (with 186k miles). I have many years of experience with auto repair (since 1974).
The brake pedal vibration/pulsation is almost always caused by one or more warped brake discs. They should be replaced NOT cut.
Your mechanic sounds like an incompetent fool. The Honda dealer should NOT refuse to work on the car just because a non-dealer worked on it. You should report this dealer to the American Honda headquarters in California.
The squeaking is probably caused by worn out shoes/drums on the rear.
All of these repairs should be routine/standard for ANY qualified Honda mechanic (dealer or otherwise). My $0.02.