Is a husband's action of threatening divorce to prevent his wife from attending a mixed party, followed by his regret over that action, right or wrong, especially after her cousin's daughter confirmed that the atmosphere was familial and respectable?

The questioner's abstention from going out to celebrate the Gregorian New Year is correct, and it was her duty to prevent her husband and daughter from going, because she is their guardian and responsible for them. She may need to strive against them and provide permissible recreational alternatives. Her cousin's daughter erred in rebuking her; rather, she is the one who erred in going out and she must repent.