There’s a lot to unpack here!
It seems as though it is a huge priority for your family to be multi-lingual. I look forward to raising my kids in a multilingual context, and it's very motivating to me to see that it can be done. I particularly love the idea of helping them compartmentalize languages.
I always feel like there’s a little switch that has to be pressed when I start speaking another language. Even when I’m just doing a reading with students, it’s easy for me to get caught up in speaking English, or when I speak a language for a while and then immediately try to switch to another, it’s harder for me to remember a word than if I had just been speaking that language from the first place.
You’ve done a good job of putting your kids in environments where their language skills can blossom.