You may want to create a many to many relationship by incorporating a third table called Details. Your Permits table would be parent to this Details table, likewise, your Construction table would also be parent to this Details table. You may want to create a copy of what you have, and in the copy, disassociate the Construction to Permits relationship, and build the many to many I've described above. In the Details child table, you'd 'select' the Construction parent record and also select a Permit parent record. This orientation of relationships allows you to establish a many to many between the Construction table and the Permits table -- done indirectly via the Details table.
Construction table >>>> Details table
Permits table >>>>>> Details table
Does this make sense?