If your dvd drive in your computer can read the mini discs, you should be able to simply copy and paste them onto the hard drive. You should have each dvd-video as a Video_TS folder containing the .ifo, .bup and .vob files.
Once there you can use Vob2Mpg to remove the mpeg2 video out of the .vob files, combine them and give you an .mpeg file. Vob2Mpg is free to download and use. It will not degrade the quality of the video. http://www.videohelp.com/tools/VOB2MPG
There are a couple of odd sounding commercial products that can edit mpeg2 fairly well. They are VideoReDo TV Suite and Womble Mpeg Video Wizard DVD. Neither are free, but both have fully functional trials to download and use for a few weeks (not sure of the exact time period on the trials).
VideoRedo is set up for tv captures, but will work well for this home made video also. http://www.videoredo.com/en/index.htm
It can import straight from dvds, so you might not need Vob2Mpg.
I have both, but tend to use VideoRedo rather than Womble. Here is the link for Womble: http://www.womble.com/ Womble has a lot more versatility on editing functions, especially for transitions from scene to scene.