I would avoid Switzerland ... but then I would be driving in a spirited fashion that is not socially acceptable in Switzerland
If you have the time to consider the detour via Austria then you can approach the Italian lakes from that direction and do the Stelvio and Rombo (Timmelsjoch) passes - start at Obergurgl, cross into Italy and head for Merano, then turn west towards Bormio. From Bormio you have your pick of the Italian lakes. Spectacular scenery all around this route, though of course the kids don't care. Possibly slow going due to car sickness and camper vans
Clearly it's going to be quicker to barrel down the motorway.
As to where to stay - I cannot help with specifics but have been there on various Stelvio trips and it's always been acceptable, even the odd place that was a bit rough. I should have thought anywhere on lake Garda or Como will be nice, and depending on how you plan to book it, you can always play it by ear (tough with the kids in tow - you probably want to know that you have somewhere to sleep each night before you leave!).
En route you won't need to stay in Holland in either direction, unless you want to?
An obvious petrolhead stop off point for the first leg would be to visit the ring ... Adenau is a nice town and we know that the Sonnehof is a good hotel and will be nice in the summer with kids, etc., for a night.
I think you need to look at a longer hop the second day - perhaps to the north shores of Lake Constance (Konstanz).
The third day will be slower going whichever route you take, so best to make that shorter - Konstanz-Como is about 200 miles.
Cheers,
Robin