Background: Mr Bosu, a killer, was driving his dog, Trickster , and a kid to his benefactor's house. He was nothing if not kind to Nathan because the kid reminded him of his mother.Nathan was stroking Trickster's ears. Trickster was nuzzling Nathan's hand. Mr. Bosu smiled at them both indulgently as his call was finally picked up.
Source: Alone, Lisa Gardner
The definition "allowing someone to have or do what they want, especially when this is not good for them" doesn't help me picture an indulgent smile. Is it a smile that shows how self indulgent Mr Bosu is? If so, would you say "smiled at them both self-indulgently"?