You could use a pipeline to create the entries in your parent table. Key Field is a text field, and every time an assignment is created, a Pipeline searches to see if that version of name and date exists. If not, create a record in the parent table with that specific string in a manually entered text field.
The child table you should be able to use the formula field in the relationship. It only fails if part of the formula is from a lookup field. If that is the case, you also make a manually entered field on the child table called 'Name and Date Manual Field'. Create a dynamic rule that upon saving the record, copies the Formula field to the manual field.
But also, I'm not quite understanding why you can't just set all the appointments in your child table, then just create a report that you filter by date or user to see the schedules?
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Michael Tamoush
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