What is the ruling on a committed young Muslim man remaining with his divorced mother who exhibits behaviors inconsistent with Islam, and is his feeling of dayyatha (cuckoldry/lack of protective jealousy) in this situation valid?

Filial piety is one of the most obligatory duties. Allah Almighty has commanded us to associate with even polytheist parents with kindness, so how much more so with Muslim parents. You must advise your mother to abstain from sins and explain the sinfulness of her actions. If she responds, then praise be to Allah. If she does not respond, then abandon her with a beautiful abandonment (hajran jameelan), and do not mix with her in a way that harms your religion, while continuing to advise her from time to time.

In summary, regarding living with her: If your continued presence with her will benefit her in her religion or commitment, or keep evil away from her, and if associating with her does not harm you, then remain with her, seeking reward from Allah. However, if your attempts are ineffective and associating with her causes harm to your religion or reputation, then there is no blame upon you for abandoning her, while continuing to check on her, fulfill her needs, and advise her occasionally.