The "job description" arrow takes the user directly to the summer work record
I don't quite follow what you are trying to do from a layout based on the Business Records table occurrence.
If you enable "allow creation" for Summer Work in the Business Records to Summer Work relationship, a portal to Summer Work can be set up to create a new Summer Work record and link it to a record in Teacher Data by selecting a teacher in the Summer Work::Teacher ID field (usually done via a value list). This should be a "mirror image" of the approach that you use to do this from a layout based on Teacher Data.
But you indicate that you are "having the ability to assign a teacher to a particular summer work record. " That leaves me puzzled as no such record should exist until you use the portal to create one by selecting a teacher in the Teacher ID field from the join table.