Even though he's not Wendy's "real" father, Wendy has always considered her stepfather, Josh, to be the true father figure in her life:
Watching Josh as he took out the jar of raisins, arranging them on Louie's plate in the shape of a man, Wendy felt crummy for saying what she had. Do you have any idea how lucky we are to have someone like Josh in our life? her mom had said to her, times when Wendy treated him the way she knew she had just now. Do you even remember what it was like before he came along? Do you think Garrett would ever put himself out for you the way Josh does? (1.49)
Because Garrett has been mostly absent in her life (not to mention living all the way across the country), Wendy has relied on Josh as her dad—and he's certainly risen to the challenge. Josh treats Wendy with the same love and care he offers Louie, his biological son with Janet. And because of this excellent treatment and open love, Wendy accepts Josh as her father and Louie as her brother wholeheartedly:
Times like that, Wendy never said he wasn't really her father. Same as she never called Louie her half brother. Somebody else did now and then—Aunt Pam, for instance. (9.45)
Other people might see Josh and Louie as somehow not Wendy's "real" family, but she knows better. When it comes to dads, Josh is the real deal.
But things get more difficult when Janet dies—mostly because Josh is so wracked with grief that he doesn't even know how to take care of himself, let alone two children. Although he loves Wendy and Louie dearly, he has a hard time parenting right after 9/11:
The music was louder now, and it pulled her down the hall, though there was another sound coming from the living room, the sound of weeping.
She saw him then, though it was hard to make him out with no light except for what came in through the window from the street. Josh, sitting on the floor by the stereo, his head in his hands, his shoulders heaving. (8.117-118)
In the end, Josh allows Wendy to go to California to live with Garrett. This isn't because he doesn't love her like a "real" daughter, but because he's so overwhelmed with his own life and grief that he cannot take care of her like she needs. Poor Josh doesn't know what to do without Janet. No one in their family does.