As you're so deeply invested in this question (given your marriage), I don't think a rundown of Lumbee history in a Reddit comment would be quite sufficient to tell you what you need to know. So I'd suggest starting with Malinda Maynor Lowery's work. Here's her faculty page at UNC, with a list of her publications. Malinda is a Lumbee scholar, a great historian, and a generous person. If you look through her work and want to dig deeper, you might try getting in touch with her yourself.

If you're interested more broadly in smaller tri-racial groups like the Lumbee, you might try Ariella Gross' What Blood Won't Tell. It's a history of law and race that's particularly focused on racial trials. Those were trials held to determine someone's race, many of them during the 19th century, and they were extremely weird. Gross might be helpful in hinting at the bigger picture of where Lumbee history fits in the larger context of the history of race in the US.

It would also probably be a good idea to ask your wife's family these questions. Lumbee culture doesn't only exist in past tense -- it's alive now. History is great, but native people don't live their lives in the past. That's probably good news for kids anyway, as they can learn about their heritage through family connections or community events rather than history books.