... I searched time machine/previous date/library/app support. There is no iweb listed. My current library/app support shows the backup...
The path you showed is the upper level of the hard disk. The file should be in your Home directory (probably aka "current library").
So, Time Machine/previous date/Users/your shortname/Library/Application Support/iWeb/
Thanks for the reply and the good advice.
Last night after posting my problem, I found where someone had a similar problem and OldToad told the person about using iVisible to show hidden files.
I downloaded the app last night, and this morning I was able to locate my backup of iWeb in a TimeMachine backup early yesterday afternoon.
After removing the incorrect backup initiated by Miltisite, I restored the good backup from TimeMachine.
I appreciate all of the help available from Apple Discussions. It is a stellar service because of the dedicated volunteers.