With the addition of webhooks and iterators, we can handle two-way synchronization using solely TeamDesk built-in tools.
After starting a free trial please visit Setup | Database tab | Tools | 3rd-Party Accounts | Google Account and authorize an account to allow access to your calendar. Save and here we go!
A more detailed description of this example is provided in the blog post: Google Calendar synchronization, take 2
Any support materials, such as spreadsheets and real-life work samples would be very helpful as they would help us better understand your business process.