A good video editor?

Audacity may work for you

video and audio, although played together, are typically edited separately. there is no video editor (that i am aware of) that does even passable audio editing. typically you need a separate audio editor. the best in my opinion is Sony Sound Forge, or Audacity if you are looking for "free". if you plan on doing multi-track editing (multiple audio sources), Sony Acid works best in that scenario.

for what you are wanting to do, the best thing would be to open the video in your editor, then make notes on what the timecodes are of the spots where you want to adjust the audio. make a list of edit points, then open the audio in your audio editor and make the necessary changes.

it is important to do it this way, because a video editor will re-encode the video when you are done fiddling with the audio and resave the changes, and this is bad because every re-encoding the video loses quality.

but if you edit the audio separately, then you can remux the audio with the video without re-encoding that video, thus preserving the original quality!

the same is true for audio, of course, and you don't want to re-encode your audio more than once, so it is best to make all your changes in one session. this is why pros prefer to work with uncompressed video and audio, so this is not an issue.