Hi Gundumummy (and I have no idea what that means by the way
If you need to commute to Tiffins but be in the Nonsuch catchment, there are a number of reasonable places you could move to. You could actually move to Cheam - which is obviously in both the Nonsuch and Wallington catchments but it is then quite a long bus journey to Tiffins. In fact it would probably involve two buses (x26 or 213 into Kingston and then a 65 up the Richmond Road), about an hour's journey.
Alternatively, you could move nearer to Kingston for example New Malden/bits of Tolworth. This still puts you firmly in the Nonsuch catchment (not sure about Wallington) and a reasonably quick journey into Tiffins.
These are both bus routes. You could of course think of areas where your DC could get the train e.g. parts of Epsom are still within Nonsuch catchment but would involve a change of trains for Tiffins. (There is a bus that goes into Kingston from Epsom but again about an hour's journey.) Obviously it really depends how far you want DC to travel. I would say for the easiest journey to Tiffins you need to be west of Nonsuch otherwise it's a pretty long haul by train or bus.
Hope that helps but I'm sure others will be along with more advice and congratulations to your DD