I wrote an Upgrade Guide a while back. It's the best guide available for upgrading any mojoPortal site.
Regarding upgrading a site with a lot of child sites, the process is no different except you need to check everyone of your sites to be sure you haven't run into any skin compatibility issues.
The presence of the custom controls means you're going to need to make sure they work with the version of mojoPortal you're upgrading to. There's no way around that unless you just wing it and hope for the best.
You don't necessarily have to take the sites offline but given that you have so many in one installation, you really should because the chances of someone hitting the site when you're still copying files is rather high. It's usually better if you give users a friendly message about updating than for them to see an error.