Hi, I feel I am missing some information but as far as selecting one assignment to show you will need to use a global with a drop down list based on the field Assignment and having a relationship to the Assignment field. At that point you can select the assignment to show from the global.
I don't understand the rest of you questions.
We need a lot more detailed information before we can help you. Let's tackle one thing at a time. Explain in detail how you go about creating the report that you have. Perhaps post a screenshot fo the script and the layout. An overview of the tables you have would also help.