I took them out of their Swiss school as soon as we found out we were moving to the US, which was late April 2011. I would've needed to pull them out for 2 weeks for the look-see trip anyway, which the school would've been very disapproving of (it's cultural NOT at all done there). Then they would've finished in June for summer, and going back in August and slogging away in French for maybe another month or so whilst we waited for visas would've seemed very pointless to them.
But the main thing was that my 11 yr old hadn't written a word in English since he was 8, and had only studied arithmetic, not the early fractions/ geometry/ statistics that the US kids do from 3rd grade or so. And my 7 yr old could barely read in English at a slow c-a-t level; I'd done the basic sounds with her, but was waiting to get her French reading consolidated before really pushing the English.
So they left late April, homeschooled through summer - we did a couple of hours most days from then on non-stop, rather than breaking for the usual 6-10 weeks - into October, then we moved mid-Oct. (We took the US look-see trip during this time, as well as one back to the UK to visit family.) We carried on the homeschooling in the US for 6 weeks, as we were in temporary accommodation waiting for our shipment, and it was going so well anyway I figured they may as well carry on until we moved into our proper house and placed them in their final local schools then. By the time they went back to school, it was the very end of November, so they'd been homeschooling almost 8 full months.
I am so, so glad we did it. I got my 11 yr old completely caught up to his US peers in reading comprehension, writing and maths (American history is still a bit shaky even now :-), and my 7 yr old went into 2nd grade with a not too disastrous reading level; 6 months later she was entirely at grade. They arrived at school knowing roughly all the right things, using the correct US terminology for things (ie, in the writing process they go on and on about main idea, topic sentence, 5 paragraph essay; they use the imperial measurement system in math, etc).
And it was very bonding. We all enjoyed it, and it brought us very close together. It was surprisingly easy, with all the great materials available online or by post, and it turned out that a moderately well-motivated child can cover as much in an hour as a class of kids would cover in a day: much of the school day is repeating for the slower ones, crowd control, moving from place to place, recapping on yesterday, assemblies and so on. If you've only got one student, you can tell after 2 or 3 fraction sums that he's completely got it; no need to assign 20 to everyone as you would with a whole class because you can't tell which of the 30 need the practice and which ones are knocking them out in 5 mins. We did a lot of history, geography and science by watching videos together and then discussing them afterwards; again, you can tell from a good chat how much he has understood and absorbed, and add to his knowledge; it doesn't need an essay or multi-choice questions.
Obviously longer term homeschooling requires more thought and planning, but as a quick and dirty way to fill in major gaps or keep them on track in a short timescale, this worked just fine, meant they got some quality time with me, and only had to start one school knowing they'd be staying and could really make friends. Plus it hasn't done my now 12 yr old any harm at all to detach 'education' and 'learning' from 'school' as a concept; ticks all those 'lifelong learning' boxes nicely. :)