I don't know why you have to spread the upgrade into three weekends. It shouldn't take that long unless you have many db servers. The SP3 upgrade I did to all db servers, with some minor problems of course, was done in one weekend. We are fully replicated environment. You need to shut down all subscriptions or just stop the SQL Agent on the subscriber(assuming it is a pull), no need to shut down the machine tough. The you shut down the Distributor, if it is on a different machine. Apply SP3 on Publisher first, then Distributor, and Subscriber. Remember to uncheck to autostart SQL Agent so replication agents won't get started incidently. After finished applying SP3, turn the replication back on. If you a certain agents fails, reintialize it. Good Luck.
Reason is that databses are really huge and We had occasion when SP3 failed on us leaving dbs in SP2.5 LOL . then we spaend 3 hrs with Msoft and installed the SP3 in Debug mode . I am being careful because we get a window between 1:Am to 5:AM only to do any changes and is too short to do all three if something doesn't go well
With transactional replication, the proper sequence should be distributor, publisher, and subscriber. The distributor should always be upgraded first. Please refer to SQL 2000 books online <\Installing SQL Server\Upgrading to SQL Server 2000: Overview\ Replication and upgrading> for details.