The unique URL that you send teachers allows them to book breaks. The URL you send parents allows them to book conferences. A teacher who is a parent will get two different URLs, one in each mail merge.
It’s important that their Teacher ID match the Teacher ID in the course roster. And it’s important that their Family ID match their child’s Family ID. Their teacher email address and parent email address can be the same, but don’t have to be.
Teacher/Parents will need to book breaks so that they can attend their child’s conference without a parent booking them at the same time. And they will need early access so that they can get first chance at signing up during the break time.
You can use the early access feature to give them a head start. Another option is to send the mail blast in stages. If all teachers have school-issued email addresses, you can simply sort or filter your parent login link spreadsheet in order to invite teachers to sign up before everyone else does.