I could be wrong, but I dont think being a cousin makes you a legacy. Every org is different though. you might want to look into that. she can still write you a rec though. only 1% of what dont end up getting a bid? legacies? even if you are a legacy, it doesn't mean you're guarunteed a bid. do NOT think that. what if there's 50 AXO legacies going through rush, but only 40 can be accepted?
i just checked the AXO website, and only sisters, daughters, grand daughters and great-granddaughters can be legacies.
http://www.alphachiomega.org/index.aspx?id=76 so if you're one of those, then you're a legacy.
dont go into recruitment thinking "i do/dont want that group." remember that they have to want you back. it's a mutual selection process. keep an open mind, especially in such a competative environment. best of luck!