@Joe_Calabrese ...
Can you please help to clarify for me... In your subject line, you say that you had a copied module that only shows up in assignments...but in your description, you say that you copied assignments from one course to another...not copied modules from one course to another. If you are copying one or more assignments from one course to another, then it would make sense that it's not showing up in your module.
How are you coping your course content? Are you using the Course Import Tool to copy specific content from one course to another?
How do I select specific content as part of a course import?
Or, are you using the "Copy To..." option?
How do I copy an assignment to another course?
Using either method, after you have copied the assignment from one course to another, you can certainly move that assignment to the proper assignment group in your course.
How do I move or reorder an assignment?
Finally, if the assignment isn't there already, you can add that assignment to a module in your course.
How do I add course content as module items?
I hope I've understood your question and covered everything. If not, please provide some more details so that Community members can continue to help you out. Thanks!