I’ve heard various arguments that there were two creations and that Adam had another wife before Eve. I don’t believe that. I believe that Genesis 2 simply details the creation of Adam and Eve. Would you agree? Or do you have additional feedback?
Put a little differently than you have, I believe resolving the differences some see between Genesis 1:1-2:3 and Genesis 2:4-2:25 is simply a matter of realizing that Genesis 1 is God’s account of the creation and Genesis 2 is Adam’s account. Viewed in that way we can see that you are correct. They are two versions of the same creation with Adam’s account containing more detail about Himself and Eve.
The false teaching that Adam had a previous wife springs from the so-called Lilith myth, a folktale that claims Lilith was Adam’s first wife and was banished from the garden for refusing to be submissive to him. God subsequently gave Adam another wife, who He made from one of Adam’s ribs to ensure her subservience. It’s called the Lilith myth because there is no truth to the story.