I am trying to find the story where the first born twin reaches back in and pulls his sibling out at birth. I believe it was a Greek myth, but it could have been from another culture.
If it is indeed Greek, you may be referring to the birth Artemis (Diana for the Romans) and Apollo. Leto gave birth to Artemis, Artemis then helped her mother give birth to Apollo. Here is a quote from Pseudo-Apollodorus, Bibliotheca 1. 21:
... Leto had relations with Zeus, for which she was hounded by Hera all over the earth. She finally reached Delos and gave birth to Artemis, who thereupon helped her deliver Apollon."
Might you have it backwards? There's the Biblical myth of Jacob and Esau. From Genesis 25.26:
After this, his brother came out, with his hand grasping Esau's heel; so he was named Jacob. Isaac was sixty years old when Rebekah gave birth to them. (NIV translation)
The idea is that the name Jacob and the Hebrew word for ankle are similarly spelled. See this article for the explanation:
The first twin emerged both red and hairy. His name, Esau, somehow describes his hairiness. The second twin is neither red nor hairy, compared to his twin, but he is also named for his first impression on his parents. He comes into the world grabbing his brother's heel. The Hebrew word for heel is 'aqeb, and so this child is named Ya'aqob, or Jacob, literally meaning "he clutches the heel." Interestingly, though, and also important, Jacob can mean "may God protect or reward," or—unfortunately for Esau—it can also mean "usurper."