If the other computer is subscribed under the same LiveID as the one you renewed with on the other PC, the second PC will renew automatically. If you mean that you uninstalled and reinstalled OneCare on one PC with a retail CD and used a different LiveID, you not will need to uninstall and reinstall on the second PC, too, and activate with that same new LiveID.
Can you explain what you mean by "installed renewal...on one computer?"
-steve