Parent-child portals are really a misnomer. In DotNetNuke you have the ability to host multiple portals under one IIS website but they do not really have a parent-child relationship.
The first portal created is the default portal (portalid=0), all portals after that are numbered sequentially.
The only place that the Parent or Child naming is used in DNN is in the UI to create a new Portal. In this UI, when you select Child Portal then a sub-folder will be created, so you will address it on the Url as a "child" folder of the main portal's Url. This just means it does not have to have it's own Domain Name and can be accessed like a virtual directory by placing the name of the portal on the Url like a virtual folder. (e.g. http://www.parentdomain.com/childname)
What is not entirely obvious is that all the portals for an instance of DNN are really being served off that same website, so if you had more than one "parent" portal (a portal with it's on domain name) and a child portal, then the child portal can be addressed by using any one of those parent names with the childname folder. For example http://www.parent1.com/childname and http://www.parent2.com/childname would get you to the same portal.
The way DotNetNuke decides what portal is being requested is by doing a lookup on the Url in the browser and comparing it to a list of PortalAlias names.
You can find more info about the PortalAlias here:
http://blogs.snapsis.com/PermaLink,guid,87c379cc-c700-4eb8-a48d-e778aeef65fa.aspx