Sync iphone to two computers without delete data

Hi everybody!

I want to sync an iphone4 to two computers, both of them running mac os X 10.5.8 and iTunes 10.

The first one, called home computer, holds apps, music, videos, podcasts, photos. I don't want to sync contacts and calendars on it.

The second one, called office computer, contains just that: contacts and calendars, and nothing else. Actually, it contains a few other items, but I don't care to sync them.

First, I disabled automatic syncing in both computers.

Then I synced the iphone to the home computer, checking all the requested panes: apps, music, videos, podcasts, photos. I unchecked just the info pane. Everything worked fine.

Troubles are coming syncing to the second computer, office computer.

I check the info pane (everything ok, so far). But when I uncheck the app pane, it appears a box asking (sorry not to be precise, I have to translate from italian) "Do you really want to unsync all apps? All apps contained in iphone will be deleted". If I choose not to sync, the multicolor bar below starts worringly to decrease, and the green part (apps) disappears.

I wanted not to sync the app in the iphone, not to delete them!

The same happens if I uncheck all other interested panes, i.e. music, videos, podcasts, photos.

The final result is a sad, short bar showing just a very small yellow strip, "other" meaning contacts and calendar.

What I have to do?