"when you type out www.p for instance, it ends up showing the full path to peachy18"
You mean on the "address" -toolbar, or on Google Seach -box? Address-toolbar can be cleaned clearing the history, Google's search -box needs to be cleared on "internet options", "Content", "Autocomplete", "Clear Forms".
Then, just install a new lightweight browser with popup-blockers etc. like "Firefox" for only your personal use (=porn) and hide a link to it. Remember not to make it your default browser when it asks.
Or, just use search engine no other people use in your family (other then google?)... search for Peachy18 and click the link and it won't get saved on the address bar.