Hafetz Haim Halachot
Halacha 122 / 215

Hilchos Lashon Hara chapter 8, section 11

It also makes no difference whether he tells the story in front of people who are not relatives of the person he is talking about, or in front of his relatives. Even a brother speaking about his brother to their father is complete lashon hara.

Even if his goal in telling is that the relatives will correct him for this, it is still forbidden. He should first have corrected him privately, between the two of them, and not rush to tell about his shame. Only if he thinks that his own correction will not help, then it is allowed.