Sucks to be a woman in an abusive marriage who takes a lover on the side, gets pregnant by her lover, decides to have the child and divorces her husband.

No, I think it works out to her advantage--husband owes child support. Even if she gets remarried to the bio-father. (And husband potentially gets visitation rights. But if he's annoyed that it's "not his kid," he may not care about that.)

The legal-parenthood situation doesn't come up unless:
--Child support is an issue,
--Visitation rights are an issue,
--Custodial decision-making (medical, etc.) is an issue.

If everyone's content to work things out among themselves, the courts don't interfere.