What is to be done after a wife's admission that the children are not legitimate, and is it obligatory to perform li'an and disavow them after confirming adultery?

The Shari'a takes precautions in establishing lineage and is strict in denying it, attributing the child to the bed. Therefore, your wife's children are considered yours as long as she is under your marital authority, and their lineage cannot be denied merely by her claim. You may resort to li'an to deny their lineage if you strongly believe her claim, or you may choose not to perform li'an and attribute them to yourself, in accordance with the hadith (definition): "The child is for the bed."