I can only speak to our experience, but I found the local parents to be quite generous with their time and willingness to open their homes as needed. I had “if you ever need anything “ offers from parents during family weekends. Just from people we happened to sit next to for one event or another.
The kids communicate and set things up themselves. They get pretty good at it.
The school coordinates on some of the bigger things (asking if people are able to take an international student over break, for example). Cate and Thacher had their communities put to the test with the Thomas fire, and they learned a lot. There is a deep well of parents who get how hard it is to have kids so far away. People will step up.
We have set up carpooling pretty easily - you aren’t strangers once your kids go to school together. It is ok to reach out to people you don’t know.
E.g. Kiddo accidentally left his backpack/laptop home when he returned to school this fall. All he had to do was look up kids in the directory who live in our area, found one who was traveling the next day, texted him (even though he was in a different grade and hadn’t really spoken with him), and the family drove an hour out of their way to pick it up from our house. 
It was amazing, but I would totally do so the same thing if the situation was reversed. Families are very generous and connected, but you don’t necessarily hang out together the same way as you would if your kids went to local school together. Ymmv, of course.
Eta: the schools have staff that coordinate travel, shuttles to airports, etc. They will help make sure travel/carpools work smoothly. They hooked us up with a carpool the first year.