There are two ways to handle navigation links; linked objects and manually defined links.
With Linked Objects the security trimming is in place. This could be a link to a site, list, or page if you are using server w/ publishing. You can configure the navigation to show all sites.
In some cases though where there are a LOT of sites, users decide to only show specific links and they will manually define the links. In this case SharePoint doesn't know the difference between a site on your server and something like microsoft.com so there is no security trimming. All users will be shown the links, and if they click on a tab that they do not have access, they will be shown the access denied screen.
It sounds like you need to step back and provide better planning for the navigation, and perhaps the overall site topology. It isn't a great idea in most cases to have a ton of sub-sites within a single site collection.