Can a temporary CORE password be sent to my personal email address rather than my work email address?

No, for security purposes your temporary CORE password can only be sent to the email that is listed in CORE.  If your work email has recently changed, you will want to speak to your department-appointed CORE Security Administrator to update your email address in CORE.  If you do not know who this person is, you will want to speak to your supervisor or department controller.