What you are asking to do potentially involves some fairly advanced editing techniques and may be really time consuming (the kids will probably have grown up by the time you do all this), and also fraught with difficulties - ensuring the audio remains in sync with the video is normally the biggest headache. However, if you manage to do all these steps, you will become an expert (or at least a well-informed beginner)!
Before you consider doing such a process, an obvious suggestion is to simply cut out unsuitable sections and any beginner could do this using a number of relatively cheap packages e.g. Nero Vision Express, Cyberlink’s Powerproducer, and this is quite simple to do. Really, when it comes down to it, this is all TV companies often do to show a program that might not otherwise be shown!
Obviously if the scenes are long (e.g. bedroom scenes), this might lose some of the impact of the story. For scenes where there is a lot swearing, then excessive editing may lead to a jerky picture I guess but you would not lose the sense of the story.
However, assuming you want to retain the whole story then here are some techniques you might like to consider using freeware or relatively inexpensive commercial software.:-
(There may well be commercial packages that will do what you are asking, but these may be quite expensive - I cannot advise on this as I have no expertise in this area).
The first thing you would need to do is to demux (separate) the audio and video sound tracks and edit these separately. DVD decrypter (freeware) or similar will do this.
Muting the sound would be relatively easy using one of a number of packages (e.g. Nero Wave Editor). You may need to convert the soundtrack from AC3 (dolby digital) to WAV format (e.g. HeadAC3HE - freeware) before doing such editing as well and then convert back at the end. However, you would also need to know exacly where to mute at all points. This could take a lot of patience.
Blurring the nudity would be more difficult I think as this would involve significant editing of a number of video frames. You could probably adjust the brightness of the picture without too much difficulty for sections that you consider unsuitable (Nero Vision Express would be a good starter - Virtualdub (freeware) con prably do this as well as far as I know).
Finally then, you could use virtualdub (freeware) to remux (recombine) the edited audio and visual streams to mpeg2 file. You would then have to reauthor to DVD format (Nero Vision Express or Cyberlink Powerproducer say).
The Nero suite of packages would help for a lot of these actions.
As you can see there are quite a lot of steps. I really doubt the gain is worth the pain in this case. However, it can be quite satisfying achieving your objective.