On a movie DVD what is the difference/use of the
English - Dolby 5.1 and/verses the English - Dolby 2.0 track?

5.1 is surround sound - five speakers required. 2.0 is only right and left speakers.

Would 5.1 Surround Sound not play in a L/R only speaker system
or just not sound as good as intended?

The reason I ask is I'm duplicating one of kids DVD's to keep the original safe.
The content is too large for Fast DVD Copy to duplicate without instructing it to
leave off some content. So, I'm trying to figure out what I can leave out.

It won't sound right, as the rear content will be lost. I think you'll lose the center speaker content too. If they aren't going to play it in a surround sound system most times, dump the 5.1 soundtrack.

So, if you are duplicating a DVD and need to save space you can safely exclude the surround sound if you have no need for it. Likewise the extra languages and Dolby.

The extra languages are always the first to go, along
with the Bonus Features that aren't always a bonus.
But in this case it still wasn't enough. I didn't want
to delete the wrong track, and have them revolt on me.

If I'm not mistaken, the 2.0 sountrack has some surround info in it. I think it was intended to give the 5.1-challenged a taste of "envelopement", though small.