On emails you trigger manually - like confirmations, accept/decline and cancellation notices - you can enter another email address on the 'To' line separated by a comma. But unfortunately there's not currently a way to send all automated messages for a client to multiple email addresses.
The one exception is the reminder. On Client > Details, you'll notice a field called "Email Cc" at the bottom. This lets another user schedule appointments on behalf of the client. To enable this, create a new record with its own email address, and then make that record the "parent." Then the "parent" will also get appointment reminders and be able to see upcoming appointments.
Note that right now you can only add one "Email Cc" for each client. If you want to remind both parents about a child's appointment, you would need to use one of their email addresses for the client (in lieu of the child's email address) and make the other the "parent." Your clients don't see these labels, though.