Hello,
About 6 months ago I went through and tested around 25 PHP/MySQL based CMS systems that didn't cost money, basically everyone I could lay my hands on that looked decent; and I found none that did child portals at all; or it required file hacks to get it to work in some crazy roundabout fashion that made no sense to me, who is not so much good with php.
I was and am more familiar with DNN when I was doing this search, but NONE of them made it clear or obvious how to add child portals if at all possible. normally it looked like there had to be some kinda 'hack' implemented to get it to work, and then it was a work around in the DB, or the file system.
In short, I've never found a free LAMP CMS system that did child portals in any way that wasn't overly complicated. Almost all of them did the last 2 bullet points, as those were basically the same 3 points I was looking for when I was going through them.
If you want to test and explore some opensource CMS systems yourself, I'd recommend http://www.opensourcecms.com/ as they have demo's available for all the systems they have up.
Not to try to dash your dream of finding one, I just never could, but if you do find one, please post back here so I can look at it. :)