Is there a good way to hotsync or synchronize datebook entries between
Palm PDA, Palm Desktop, and share360?  Specifically, I'm looking for
user's experiences with Sony Clie PEG-TG50 which is a Palm-based PDA,
and Sony's version of the Palm Desktop, and share360 which is a
corporate scheduling software similar to meetingmaker.

The official word from cybozu who makes share360 is that the only
supported sync is using share360's provided conduit, which goes direct
from share360 to Palm, completely bypassing Palm Desktop.  This is not
satisfactory to me because share360 doesn't handle conflicts well, and
I want to be able to see my schedule on my laptop's screen without
being connected to share360.  I  prefer to sync PDA with Palm Desktop,
and then do a second sync between Palm Desktop and share360, and then
a third sync between Desktop and PDA.

Many in our office are doing something similar, using using
intellisync and Outlook instead of the Palm Desktop.  This worked well
for me until I had to send my PDA for repair.  Then all entries were
erased from Outlook and share360, couldn't restore.  When I asked
share360 about this, their reply was that the only supported way to
hotsync with palm is to use the share360 conduit.  The
PDA<->intellisync<->outlook part breaks the
 PDA<->intellisync<->outlook<->share360
synchronizing chain.

So, currently I just sync between PDA and Palm Desktop, and I update
from share360 to Palm Desktop manually by looking at two screens.  I
would prefer to automate it.

I'm looking for user experiences with this and/or any kind of 3-way
sync in which the "primary" sync is between PDA and Palm Desktop, and
then a "secondary" sync between Palm Desktop and other software such
as share360.

It's too bad you can't use Outlook for your base instead of Palm
Desktop... You could use
http://www.share360.com/supportcenter/s360v2/installation/installindex.cbml?volumeID=153
information to replicate information from share360 to Outlook, then
use Intellisync to handle the palmdesktop/outlook/pda sync.

I've used some multiple-syncs before, including Yahoo! (and formerly
Excite TrueSync) and had some success with them.

PS I know you said you tried this and lost data, but realistically,
what your Palm doesn't know about syncronization with share360, won't
hurt it. As long as Outlook knows what's what, Intellisync can handle
the rest faithfully. It's always good to backup data before syncing
anew, but your encounter was a one time thing. Intellisync's product
is one of the best out there, and they wouldn't survive if they lost
data all the time.

I'm also concerned about losing share360 data, because that would
affect everyone in the company who has a meeting with me.  This is why
I'm asking on google-answers before retrying the 3-way sync again. 
Thank you for your answer, though: to date, it still seems that "via
outlook" is the best way to go.