I agree with David-- Paris would be great.
London will be cold (...well, to be fair, I'm from southern California), but I could see there being lots of cool stuff indoors for kids (Museum of Natural History, Harrod's toy store, slides at the Tate Modern, maybe the Globe Theatre).
For me, it would be really hard to choose what to see in Italy with just nine days (two weeks would be better to allow time for Rome, Florence, and Venice). Also, stuff like the Roman ruins and Pompeii might be really great for the kids in a few more years (particularly the nine-year-old, since I think kids usually learn about Pompeii around age 12.) I'm not sure about Amsterdam, either; it seems like a more adult destination to me (although Holland is beautiful.)
I haven't been to Spain or Luxemburg but people say Barcelona is wonderful. Not sure about with kids, but it's definitely high on my list of places to see.