What you want to do would not be considered dual enrollment. I know in NYS, even with online courses, they have to be done by a vendor approved by your school district (in my case, it would be the NYC DOE approved vendor. Even then, the course would have to be overseen by a teacher from our school who is licensed in the subject area in order for a student to receive credit).
What you did is go out on your own, register your child for a class and now you want your school district to give your child credit for the course. It does not work that way.