jQuery dialog is duplicated when set on a form that uses AJAX
The behavior you describe is not related to the dialog function. From your provided code you can see that dialogs are created with all elements that have the identifier ".my-modal".

So I suppose within your AJAX call the original dialog element is not replaced by another version of the dialog, but a further element having the class "my-modal" is added to your markup.

You should investigate your AJAX callback function, whether it replaces the original markup or adds elements.