Another note.
kudos for taking your kids to Europe.
Rather than thinking about all the driving, flying, etc. have your girls sit down TONIGHT and each pick a place of primary interest and plan what they want to see or do there. Have them pull up images of Paris and Versailles and Barcelona. Look at pictures of Gaudi's park and cathedral.

Do you have airfare booked?
If not, then consider possibly postponing the trip so you have more time to plan logistics.

Try for more than a week - almost not worth it and can really only visit Paris and 1 or 2 other places. How about London and Paris and take Eurostar train in between - under the Channel via tunnel - just 2 hours London-Paris. Fly into one and out of other.

The OP is now going for two weeks.
If the OP can give up Switzerland,
London & Paris would make a great combo with Day trips, perhaps with someplace in Belgium or the Netherlands. So would just Paris and Barcelona with Day trips or a stop in Southern France.
They don't have much time to get organized though, and we don't know what tickets they have.

>>Try for more than a week - almost not worth it and can really only visit Paris and 1 or 2 other places. How about London and Paris and take Eurostar train in between - under the Channel via tunnel - just 2 hours London-Paris. Fly into one and out of other.<<

Pal: read the whole thread. One week is not the issue now. Significant update/modification/details since the OP . . .

Yes with 2 weeks you could do about 5 bases max and that's pretty fast but you seem to be OK with that and that's fine. Take trains though as Switzerland and big cities are best by train and you can cover more ground with trains blasting along at speeds up to nearly 200mph.

That sounds interesting. i might actually do that take the crazy trains but would they go through mountains do you know?

Read this: https://www.seat61.com/Swiss-trains.htm

Especially the section on scenic trains.

https://www.fodors.com/community/eur...trains-571126/

Little old for data but scenic train routes never change.