What is the ruling on vowing to pray a thousand rak'ahs if the father divorces his wife, and the divorce has already taken place, and is it obligatory to fulfill the vow given the existence of another vow to terminate the first vow within a specific period that the questioner was unable to fully fulfill?

The first vow, which is conditional—performing a thousand units of prayer if your father divorces his second wife—is binding. This is based on the hadith (definition): "Whoever vows to obey Allah, let him obey Him." Since your father has divorced his second wife, you are bound to fulfill it.

As for the second vow, which is time-bound—performing the thousand units of prayer during the month of Ramadan (definition)—if you delayed it without a valid excuse, you have sinned and are obligated to make it up. You are not required to pay expiation according to the most preponderant opinion among jurists. You must hasten to complete the remaining prayers and repent to Allah for the delay if it was without a valid excuse.