I don't know how you checked your backlinks, but the link: command in Google is totally unreliable. one month ago I lost nearly all backlinks according to the Google link: command, but the rank of the page didn't go down. Now with the Allegra update many backlinks are back, but rank is as usual.
If you think your links are useful for a site visitor, just keep them there. You could think of removing the duplicate content anyway. As Google might be smart enough to detect it even if there is no heavy interlinking between the two sites.
I link one way with two sites on the same IP. I dont see it as a problem, and my impression is that google doesnt. What value it gives to these links is not clear to me.
If you have a healthty supply of links for the main site , then you could remove the links or use the nofollow tag on the small sites links.
As regard the dup content , probably not a good idea and id do everything to stop google finding it on the smaller site. Dissallow, NOindex , nofollow etc.. it may even be worth while trying to change the file names just to ensure that there is no chance google , finds , sees and tags as dup the content on the smaller site.