Where's the trust? Why compare him with someone else from her own past experience? And she should ask him first if he had done something like selling properties, pawning things, loans, or anything money related just to supply the gambling habit.
She found out about his hobby so what? We, men, don't need them to be supportive of what we are doing, as long as we don't cross the line. That's where they come in. I have been gambling for years too and my wife doesn't actually care what I gamble as long as I am responsible, can supply them with their needs and a little luxury. Now that's trust.
Maybe she is just exaggerating because of his previous experience, like a trauma, but it can be fixed thru explanation. They won't go farther if your cousin stops and won't be happy anymore. Worse, he will hide the hobby and it leads to an unhappy relationship filled with fights.
Not all gamblers have the same way of thinking and on how they deal with their individual issues. If her brother ends up a gambling addict, it’s because he chose it and the way he responded to it leads him to a more serious gambling addiction. But her brother and his fiancée are way more different. Your cousin knows how to handle his gambling addiction and it even provide him as his side hustle. So there’s no reason that he should stop gambling, as he can still in full control of his life and on his relationship with his fiancée. Otherwise, if he will stop gambling to save their relationship, it only means he agrees on the assumptions of his fiancee.