Arthur was actually thankful that Belle came right on time and took the matters in her hand from him because he was not in his right state of mind. He was also glad that Trixie talked to her first because he doesn't know what he would do if he was the first one to find out what happened to his sister that past year.
Both he and Trixie were not in their right state of mind and if the two of them talked first, things might have gone out of control.
When Belle told him everything that Trixie told her, Arthur had only one thought in his mind. And that is not to return the gold to Adriano but to drain him off of his wealth before he drains the life out of him. Thankfully, Belle was there to calm him because if it was Trixie who told him that, Adriano won't see the sunset.
Among the three of them, Belle was the one thinking straight. She even managed to drag Arthur to talk to J which gave them a better solution at the end of the day.
