When a person book through my website, it doesn't show up in Square appointments, it has caused double bookings.
I'm assuming you mean your website not hosted through Square? If so, do you have your Square calendar imbedded into your website?
The only way this could happen is a user error - either on your end or your client's. Let's see what we can do to help! How do you have your online booking set up? Are client's booking directly from your Square Site or do you online booking embedded in your website?
Square Community
Square Products