Nick's distant family relationship with Daisy (second cousin once removed) does not come up between Nick and Gatsby when they meet or later. Nick meets Gatsby for the first time when he is with Jordan Baker at one of Gatsby's parties. Nick falls into a conversation with Gatsby without realizing who he is. Gatsby learns that night that Nick is his neighbor, and he has learned previously that Jordan knows Daisy. Jordan doesn't realize Gatsby is Daisy's young lieutenant from Louisville until she spends a private hour with him that night at the party.
Gatsby's plan then falls into place. He will work through Jordan to ask Nick to arrange a reunion with Daisy. When he discusses this with Jordan, she tells Gatsby that Tom Buchanan is Nick's friend, which almost makes Gatsby "abandon the whole idea." She does not, however, mention Nick and Daisy's being distant cousins. When Nick asks Jordan why Gatsby didn't simply ask him personally to arrange a meeting, Jordan explains:
He's afraid. He's waited so long. He thought you might be offended. You see he's a regular tough underneath it all.
In referring to Gatsby as "a regular tough," Jordan is speaking ironically. It is clear that Gatsby is vulnerable and sensitive in ways that might not be obvious to those who do not know him. Jordan also explains that Gatsby absolutely does not want her to arrange a luncheon for him and Daisy in New York:
"I don't want to do anything out of the way!" he kept saying. "I want to see her right next door."
It is true Gatsby wants Daisy to see his mansion, but the nature of his reaction suggests he does not want his meeting with Daisy to seem tawdry or common. Gatsby's emotional investment in seeing Daisy again is enormous and quite romantic.