What is the ruling on this girl's engagement to another man, and is it permissible to retract the promise they made to me regarding her return after the divorce, and do I have the right to claim her?

Ask the Lord to grant you a righteous wife, and resort to Him, for He answers those who supplicate Him, as Almighty Allah says: "And when My servants ask you, [O Muhammad], concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me [by obedience] and believe in Me that they may be [rightly] guided." If the girl and her family requested divorce without justification, they have done wrong, for the Messenger of Allah (peace and blessings be upon him) said: "Any woman who asks her husband for divorce without any sound reason, the fragrance of Paradise will be forbidden to her." It was your right to refuse to divorce her until she ransomed herself from you. The girl and her family fulfilling their promise to return her to your marital bond is recommended but not obligatory, and lying is forbidden. After her divorce, she became a stranger, and you are not permitted to propose to her if someone else has already preceded you. Do not cling to her, for there are many other women, as Almighty Allah says: "But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not."