I’m assuming that it’s been pretty obvious how Hook/Emma might change the past, it just took me a while to figure it out.
They are walking along the road, and see a fallen tree and a carriage approaching. They help the driver move the fallen tree, so there’s no need for David to leave the carriage, and no opportunity for Snow to steal his jewelry. David waves thank you as he and Abigail continue their journey. Snow jumps from her tree after the carriage passes and says something snarky to the duo who has just foiled her jewel heist.
Emma realizes that she has changed the past by interrupting what would have been her parents first meeting.
That is a brilliant theory and quite possibly the correct one too.