Hi, nice to meet you.

why we weren't allowed to just go anywhere we pleased without passports and permissions, while birds could just fly wherever they wanted to.

Exactly... unfortunately, that would remain a dream :).

Basically she does science experiments most of her days. 😆 Homeschooling turned out to be the best choice we could have made for her.

It might be the better choice for ours as well, we'll see how things develop later. We'll just try to provide her the best we could offer.
At least in the Philippine we have the options to do so, if she wishes to study at home.

We too moved countries when my daughters were small (5 and 7). I never had anyone try to tell me I was bad for uprooting them from their home country,

Well..why must we see it so negatively anyway?!
Travelling the world...learning about another cultures personally etc is a very precious experience that is somehow..in fact...even a privilege for most people. The children will have broader mind instead.
Such experience can't be valued with money.

however, my in-laws found it hard when we left.

That's understandable... Letting go of children would always be hard to accept for every parents :).
My parent had it hard as well when I decided to move to Germany for my husband. Now it's my in-law who has to deal with the same feeling.
It's not an easy decision, but everyone has a choice to make afterall 😊.
Anyway I believe that for our child, wherever its parent are is home.
She would feel happy as long as we're there for her.