An orthodox woman is being accused of not being Jewish after the husband decides to use as loophole to annul the marriage even though he has child with the wife. Can the Beit hadin make a ruling on such a matter during Bein hametzarim?
This sounds pretty sad.
Regarding your question, the Bais Din can give a ruling on such a matter during bein hamitzarim. The type of court cases that we don’t have during chodesh Av are a court case against a gentile, because of bad mazal but two Jews are the same for this and it is permitted.
May Hashem help you with everything you need.