Does the Edwards Love Child Have Rights?

Jess [1], here's what interested me yesterday. (Besides the Dave Matthews band detail. Now that's a way to abuse your power in bed: "No, honey," he says seductively. "I didn't mean the CD. I meant the actual band.") This story seems to be breaking open new legal territory, with the argument that hush money to a mistress might have to count as campaign donations. But then there's this other Bleak House [2] twist. At the end of the Times [3] story was this interesting passage:

It could also shift Ms. Hunter’s image from that of a predatory celebrity stalker (Mrs. Edwards told Oprah Winfrey [4] that Ms. Hunter met her husband after waiting for him to come out of a New York hotel and telling him, “You’re so hot.”) to that of a mother concerned about her child’s rights.

Several questions: Do we believe that's what she's after? And is this common legal territory, seeking "rights" for your child from a father who won't acknowledge her? And does "rights" mean something more complicated than financial support. Legal ladies, please advise.