Welcome to the Q&A Forum

I agree

Theoretically if the links make sense you should go for it but if it seems unnatural you should remove the links that are pointing to your network sites but practically i have seen that this actually hurt the SERP rankings especially when the link profile looks something like you said! In my opinion, ideally if possible remove the links and get some quality links to those websites but if you think that  removing a link is not the option then you left with no-following the links only and you should go for it! Hope this helps!

Good points, we don't doe Adwords so I can knock that out of the equation but we do have some redirects going to some of our main pages so that could very well be the reason. I'll definitely review the other points you made to see if they fit in this equation.