After much travail my Mac is once again whole.
The initial problem was the failure of MobileMe's "Back To My Mac" to start. (No green light.) That was followed by Safari loading some websites without graphics, and asking endlessly to verify security certificates. (Firefox was fine on that score.)
Two attempted re-installations of Safari (one downloaded, the next from the Snow Leopard disk), failed. I followed this with a failed reinstall of the 10.6.2 Combo Updater downloaded from Apple.
Finally, a full install of 10.6 from the Snow Leopard disk fixed all three problems, with no complications arising from applying the 10.6.2 Combo Updater and the subsequent software updates.
Exactly what was the source of the problem remains a mystery.
I did discover an additional and simpler way to do screen sharing with the Finder's Command-K (Connect to server…) capability. (It may be faster than using MobileMe.) Tech support for my sister should now be a bit less irritating to her. ("Show me, don't tell me.")
Back in business. Thanks all for your suggestions.
