You'll need mpeg editing tools. You should look at some of the products from Womble: http://www.womble.com/ Some of their tools also include authoring capabilities.
Or if you just need to cut out sections of an mpeg file, I use VideoReDo. www.videoredo.com I don't believe VideoReDo handles mpeg in dvd vob files very well though. You'd have to them in one big mpeg file. There is a free little tool that can do this for you, with the creative title vob2mpeg: http://www.videohelp.com/tools?tool=VOB2MPG
Of course the easiest way is to capture to mpeg in the first place, instead of dvd vob, but I do this with the computer and a capture card, so your listed equipment won't do that.
Once you have the mpeg files edited as you like, you'll have to put them back into dvd format (vob ifo bup). For this you'll need an authoring program. There are some free ones available, like dvdstyler and dvdauthorgui. Look over at www.videohelp.com for some guides to their use.
Videoredo and the Womble products have fully functional trials available for download.
If you have any problems with audio/video sync, try the Quickstream fix tool in VideoReDo. This usually works very well.