P.S. I will politely disagree with you on this point:
H has an obligation to pay for his mistake in the form of child support
I'm ASSuming when you write "child support" that you're refering to the financial kind. H has an obligation to the child, but it doesn't have to be a financial one.
I also disagree about the child not being able to have both parents readily available; regardless of *which* parent -- or both parents -- the child is with, she is the product of an affair. Just because the child is in one home -- or both -- doesn't mean that she will or will not find out she is the product of an affair.