As a parent who has been through this with two children and multiple bikes, I would definitely choose the dual sided pedal option (sometimes called "campus pedals"). This has the advantage of needing to only change the pedals once, and not having extraneous parts that can easily get lost.
I've personally tried the adapters and never found one I was particularly fond of. When dealing with a child's bike, I would want to avoid anything that could easily get lost.
The option to swap out the pedals would be my second choice. It's not hard to do. But it does have a couple drawbacks. You are again dealing with extra parts that can get lost. As well, it's easy to mix up the sides, or cross thread the pedals, and now you are dealing with replacing the crank arms. Finally, most 9 year olds lack the leverage to loosen a tight pedal, so you are going to have to be the one switching them whenever they want to change the ride.
I actually use campus pedals on my main commuting bike. That way if I ever decide that instead of riding the whole way home, I am going to take the train to the closest stop and just ride the last 2 miles, it's easy to do in street clothes with my normal shoes.