Hi all, and thank you for previous help.
We are moving to the Geneva area in late September. My wife is a diplomat with the UN, I've largely been a stay at home dad (retired school teacher and formerly in business).
We plan to live in Vaud, for a few reasons, it's beautiful, it's on the correct side of the lake for the UN, we'd like a house with a garden (but are not rich).
We are still deciding between having our eight year old attend school in public school or at the local international school (Le Chat).
Our eight year old is fluent in English and Japanese, has attended IB school in Japan for several years. She is social and seems to make friends readily.
We don't have an house chosen yet, but would like her to start school pretty soon.
From what we've gathered, the CDL (carte de légitimation) vital to our life. My wife, the diplomat, has heard that it will take about a month to be issued. I'm a US/Irish dual passport holder, and expect to be in Switzerland on the Irish one.
My questions include:
Can we register our daughter in public school (Vaud) before/without the CDL?
What do we need to have to register her?
Is it okay to start her in October?
We've heard wonderful things about Swiss schools tutoring/fast tracking non French speaking children at public schools. Knowing that in reality ESID (every situation is different), as a generalization, is this pretty much the case? Will she be assigned a remedial teacher for French immediately or is there a process? Do most schools have some staff there that can help?
We'd like to have her learn French if possible, but also to become friends with local and nearby children.

Our other option is Le Chat, which looks like a wonderful school, and would be a fairly smooth transition (IB, our daughter is "international", and English being readily available.
Of course, it's pricey, and she will probably not know the neighborhood children as quickly, and there will be a commute.
I didn't see anything about CDL required for her to start school, and am under the impression that since it's an international school, so long as there's some ID (passport) for the child, and the tuition is paid, they would be more flexible during our transition period (locating a house in the area, getting a car, waiting on CDL.

I'd really appreciate answers, advice, personal experiences, and information that you can provide. Thank you very much.