Well, you could make a copy of the database, remove the sensitive information, and post that, but I can offer up at least one suggestion without getting into it.
Create a query to identify where there are part numbers in "Part table" and not in "Labor" (join part number; include all from Part; pull down both Part Number fields; set Criteria to "Is Null" in Part number field from "Labor"). Use that query as the base to Append to the Labor table. You can have the queries launch when you load the Labor form.
EDIT:
Code to launch query on load -
Code:
DoCmd.OpenQuery "YourAppendQueryNameHere"