How do I change the email address that iCal alerts are sent to?
The simplest solution would be to add the address to which you want alarms sent to your Address Book entry. Beyond that, I don't have an elegant workaround, but you could, for example, run a script that could contain a variable to send alerts to multiple recipients.

I sympathize in that it's annoying that your Address Book entry is forced to contain a mix of public and private information used for various, and differing, purposes. This is one of Apple's many decisions that (I assume) works for the majority of the user population, but bites the outliers in various ways.