Why are Billy and Victoria being so selfish, give the baby Lucy to Phyllis?

I think Daniel is going to sign over rights, then Phyllis is going to get some sort of custody over Lucy and then Daniel will change his mind and want to be her dad. I hope Billy and Victoria lose Lucy because they got her illegally and any court of law would side with the grandmother over someone who bought the child, even if they bonded with her. I really hope Lily talked some sense into Daniel and he really doesn't sign over rights, I think he'd be a great dad.