Why is "odjíždět" used here and not "odjet"? As far as I understand the English sentence it describes a one-time situation and nothing habitual.
Perfective vs imperfective.
The English isn't perfect, it is past progressive. While he was in the process of leaving, she was sad. But once her father was out of sight, she played with the other children.
Is it possible to use "až" in place of "když"?
No, at least not here. It is hard to find good use for "až" in the past. Those I can think of are translations of "until", not "when".