Yeah Ann, I know all about that. But "The Queue" requires advanced planning and of course a great deal of patience. I sometimes get the impresion when people mention Wimbledon here - especially months in advance befoe the Public Ballot has been run - that they can just turn up on the day and buy a ticket. Doesn't work like that.

Too many places for 18 days, especially because you are trying to do it all by train travel between cities.

Gordon R - you may know all about the queuing and the public ballot, but chances are that the OP didn't.

my comment about queuing was tongue in cheek but the ballot is perfectly feasible for the OP.

got to be in it to win it!

Day 1 - arrive london. Check in, try to recover from jetlag. I'm assuming you're from N America]
Day 2-4 - explore London.
Day 5 - eurostar train to Paris. stay 4 nights - gives you 3 days.
Day 9 - train to Interlaken/Wengen Stay 5 nights
Day 14 - train to Venice. stay 4 nights.
Day 18 - fly home.>

I like annhig's tweaking and if can't extend your trip chose either Venice or Rome

but if you could add say 3 days in you could then stay 3 days in Venice and 4 days in Rome (3.5 really).

But annhig, as usual, makes a salient point about traveling with young kids - allow more time than without to get to the station, etc. And bring things that will keep them busy on longer train rides!