Share iCloud Family Calendar with Outlook
First, I am assuming by "Outlook" you mean the Outlook email client application and not an @outlook.com email account. In other words, your work computer uses the Exchange/Outlook system for emails, calendar, and so on.
If so - and assuming your IT department would permit this - you could try the iCloud Control Panel on your work computer. This add-in for Outlook will sync the Outlook email app with your iCloud email, calendar, and contacts - including your Family Calendar.
Instructions can be found on Apple's website. Good luck!