We are also moving back to Richmond from overseas this summer. My kids were in Vineyard before (hopefully the youngest will go back again). I remember that there was always a lot of movement each year. There are a lot of international families who move at short notice - both during the year and especially over the summer, as well as the usual migration out of London.
My son would be hopefully going back into Yr 4. A year ago they had a long waiting list and the person at the top of the list lived only 300m away from the school. Now they have spaces and no waiting list - but Yr 6 is full. So it's very fluid.
Fundamentally, it depends where you're moving back to. The waiting list is based on distance from the school, rather than a 'queue'. So if you're moving back to an address close to the school you may jump to quite high on the list - and if someone then moves into an address closer than yours, they'll leapfrog you. Which makes it even more predictable.
One thing to consider is whether you might be able to come back during the summer term, rather than waiting until 1 September. People do move their children over from other schools, but a lot of them only want to do this at the start of the school year. Sometimes people leave during the summer term, and if you're able to take up the place straightaway, you're in. Talk to the school, but if you've got the option to move during July it might help.
Good luck - and remember that all the local schools are good; so as long as she gets a place somewhere, your daughter will thrive in Richmond!