There are probably a few ways to crack this nut, but I'll just give you the steps based on my situation. I have the company ipad, android personal phone, and a Chromebook.

1) In your Apple calendar, hit the "i" next to the MiCrew calendar on the left side. Toggle Public Calendar on. Hit Share Link and email to yourself.
2) In the desktop version of your Google calendar, open Settings-->Add Calendar-->From URL, copy and paste the URL into the box and you should be set. This adds a calendar and now you can copy events to your family calendar just like before.

Like I said above, Google only grabs the data from your Apple calendar at whatever interval it feels like, so you'll have to be patient until it syncs. I've researched online and I'm pretty confident there's no way to change or even see what the update interval is. I don't think it's ever taken longer than a day. Usually the next morning it's updated. I can't remember where, but there's a setting you can select in Google calendar so that it emails you when it pulls in new events, too, so you don't have to keep checking.