Loyd's family is Apache, Pueblo, and Navajo. They're scattered all across the area from Grace to Santa Rosalia Pueblo, and most of what we know about them is that they're a bunch of sweet folks. The most important member we meet is probably Inez Peregrina, Loyd's mom. She approves of Codi, although she does not approve of looking like a Navajo, and she makes awesome bread and posole.
There's also Loyd's sister Birdie; his Aunt Maxine Shorty, who gets Loyd and Codi into Navajo land; and his Aunt Sonia from Grace, who has left Loyd a peach orchard of his own. There are more sisters, a niece, and a "naval mother" who cut the cord when Loyd was born.
All in all, as Codi notices, even though at times his upbringing was difficult, Loyd has always been surrounded by family and by love.