Let's examine the FACTS, shall we?
First, Marriage is a Legal Binding Contract (hense the Royal pain in the a$$ of getting a Divorce). At the establishment of the said contract, certain assurances of fidelity are made, before witnesses, which establish the contract on very clear terms.
If the "wife"/"Partner" is running around, willfully violating that said contract, without the knowledge and consent of the "husband"/"Partner", she has violated the Contract, both verbal and written. Why should she be entitled to anything? I would propose quite the contrairy, it should be the Violator who is held responsible for costs and damages
Her actions amount to Fraud, which in ANY other Contract situation would make the violator 100% responsible for violating the contract, and any damages from that violation.
Including any Bastard children which may result from her willful violation of the marriage Contract.
Sorry M'Lady, but simply because there are children involved doesn't move me one iota. The unfaithful "wife"/Partner" needs to accept her responsibilities, which include the costs of raising her children. If those responisibilites are to much for her then she needs to address that with the said "sperm donor" and leave the real victim of her actions alone to get on with his life, without her dipping into his financial resources, thereby rewarding herself for Fraud, and flagrant violation of a written/verbal contract.
If she is unable to accurately identify the "sperm donor", to bad. Maybe she can work two jobs, since she obviously had more than just a bit too much time on her hands before.
Sorry to sound like Scrooge here, but no other area of Law can Fraud and deceit be rewarded with monthly payments from the victims of that Fraud, and the perp be the recipient of that reward.