I have done the opposite commute for years and it is horrendous. I wouldn't underestimate it! It has got much much worse recently too, I think because there are so many new builds in Wandsworth.
Lots of fantastic schools in Wimbledon - some of the best anywhere - and from having done it I wouldn't put my children in a school so far away from where we live. We're not making the same mistake again!
Good luck, it's super hard to make the right choices x