The only real difference in FileMaker between a one to one and a one to many relationship is that you only have one related record on the child side of the relationship. You can still use an auto-entered serial number for the parent record and copy this value to the child table when making a new related record. With allow creation of records via this relationship and a set field step, you can even do this automatically from the parent table's layout. A unique values validation rule on the child record's key is definitely a good way to ensure that one to one doesn't become one to many.
I have one transaction (from the parent table) linked to one print job (child table). I was reading your post and don't understand about "copy this value to the child table when making a new related record." Right now, I have a one to many relationship in the relationship table and that is not correct.