You do not need a third party calendar to do this.
If you have a calendar at Main site 1, and you want it to be displayed on site2 and site3, you just need to import the feed into it.
You can do this by going to your main calendar on Main site 1 where your events are, and right click on the subscribe button underneath the calendar. Select "Copy Link Address"
Next, go into your site2 and site3 and go to your dashboard>events> calendar feeds
Paste the link into the iCalendar/.ics Feed URL box
Next, select "add new subscription" and "refresh"
If you do this on both site 2 and site3, your events will be imported automatically.