If I have full physical custody and shared legal custody of my children, how do I get full legal custody as well?

You can file an Order to Show Cause (court form) requesting a modification of custody and a supporting declaration stating the facts supporting your request for a modification of custody.  File these documents along with a proof of service with the court and serve your ex by mail with a copy of these documents. 

When you file an Order to Show Cause with the court, the court will schedule a hearing on your request for modification of custody.  Since you already have physical custody and shared legal custody, the court might be reluctant to grant you full legal custody; however, the court's decision would be determined by the issues in the case.

Check with the court clerk before filing the above documents to be certain you have filed all of the appropriate documents because the required documents may vary from state to state.

As for the proof of service, you can either use a court form proof of service or you can write your own.  The proof of service verifies the date of mailing your documents to your ex.  If you write your own proof of service, it just says that you are at least eighteen years of age and the attached documents were sent via first class mail unless stated otherwise to ________ (name and address of your ex) on __________ (date). You sign and date at the bottom.  The date you sign should be the same as the date of mailing and the same date you file your documents with the court.