Since you both use your own Square Accounts - unfortunately I don't believe there's a way or feature that could do what you have in mind. Maybe going outside the box with your own setup would work - one possible solution - you could create a Form or Calendar and share it between both people using a Cloud service like Dropbox. The Form could simple be a Text type file that could be easily edited - then either you or the other person would need to setup a Dropbox Account (which can be done for free) - setup permissions and share the link - this way you both have access to the Form and both can update it as needed.
