How do I deal with my mother who messages young men and speaks to them in a way that displeases Allah and His Messenger, especially since I cut ties with her when I discover this, fearing that I would be undutiful, and she refuses to marry after my father's death?

Continue to forbid your mother from evil gently and wisely, and explain to her that her refraining from marriage out of loyalty to her husband, despite falling into sin, is a great flaw and an injustice to herself. So, either she patiently endures the loss of her husband, remains chaste, and abides by God's limits, or she marries to keep herself chaste. And supplicate for her frequently.