Do you have windows XP, with Windows Movie Maker? Might be a cheap (free) way to do it there.. I've used it a lot, lots of cool special effects you can apply to kids movies, I'm sure "brighten" is probably one!
try virtualdub. free and easy, but you may not be able to save back to mpg. you can always re-encode back to mpg though. not sure if you just need the video brighter, or whether you need it in mpg.
You should capture to a DV AVI file instead of MPEG. If you start out with a MPEG compressed file, then brighten it and save it as an MPEG (which means recompressing it again), the image quality will be lower than if you went straight from the AVI, brightened it, and saved it as an MPEG.
Connect the camera to your computer's Firewire port. Then use WinDV to copy the video from the camera to the computer. This method will give you an exact copy of what is on the DV tape.
(There are other programs you can use besides WinDV, but it is the best one that I have used, and it is free.)