3 weeks trip to Western Europ

Three weeks may seem like a lot, but when you're trying to see half a continent and you've got eight cities on your agenda, you're actually already stretching your time quite thin. When you subtract out your 7 travel days plus your arrival and departure days, you're left with just 1-2 full days per city. If you know you don't mind traveling at such a fast pace, then go right ahead. But at the very least, I wouldn't add any more to the list.

That's really too much for a 3-week trip. You are covering a lot of territory, which means--as already mentioned--a lot of time lost to travel. I'd start by dropping Monaco and Pisa, which pale beside your other destinations. But you still have a string of cities that mostly need at least 4 days each, which you do not have.

If you try to take enough clothes for a 3-week trip, you'll be miserable every time you have to switch cities, because you'll really struggle to manage the suitcases. You need to plan to do laundry periodically or send it out. Which is another reason a trip moving at this pace is ill-advised.

If it were my trip I would delete Monaco and Pisa as someone else said. I would also skip London in place of something else, I didn't enjoy London that much.

Yes, in three weeks there is no room in here to really take your time and discover something nice off the beaten path.

For example, I travel every year for one month and often cover far less territory than this.

Consider finding a region or country and concentrating on it for three weeks. You can't enjoy a trip if you feel like it's your only chance to ever go to Europe. Assume you will be back!

a suggestion: focus on circling the mediterranean.
Valencia, Barcelona, Nice, Monaco, Cinque terre, Rome.

Wonderful!

You asked about what a good amount of time is to stay someplace.

Of course that really depends, but with a family of 5 I'd say it is not worth all the sturm and drang of moving from one place to the next to stay for less than 4 nights (which is 3 days). Paris and London deserve 5 days, (6 nights) I think, because you are just not going to be able to cover a lot of ground and there is a lot to see and do.

So I think you can see 4 places or so, and where really depends on your priorities.

Consider also that life will be easier if each destination is within a 3 or 4 hour train ride of another. Sure, you can fly, but it will take you most of the day. I wouldn't want to do that more than once on a 3-week trip. Fortunately the trains are great so you have a lot of choices.

Have a great trip! But don't skimp on the planning.

I would suggest that your trip is too ambitious and your children are likely to find it too much (I would find it too much!). Why are you trying to fit so much in?

Monaco is a rich playground, there's not really much to see especially for kids. I'm spending 10 days in Nice this summer and even then I have no real desire to pop across to Monaco so it beats me why someone wants to travel so far and attempt to squeeze it into a tight schedule.

My wife and I spent a couple of hours in Pisa on our return to the airport from Florence. The town is pleasant enough but nothing spectacular and the tower is simply that....a tower that happens to be leaning. You'll probably spend 20 minutes looking at it and then deciding what to do next. It's interesting enough to visit if you want to kill an hour or two before your flight from the airport as it's a 30 minute walk from there but I certainly wouldn't make it a visit in its own right.

I'd skip London too. It's far too big a city and full of so many sights that it needs at least a week to do it any sort of justification. There is no way you can "do" London in a day or two.

I would suggest Madrid, Barcelona, Rome and Venice as those would benefit from a number of days spent at each one and I would suggest a minimum of five for Rome. Either that or spend three weeks between London and Paris.

With your schedule you're not going to experience anything other than the hassle of constantly travelling. You'll be able to say you've been to X, Y and Z but you wouldn't have experienced the culture, soaked up the atmosphere or actually visited the sights for any meaningful period. For me, I don't see the point in travelling like that.

You don't say how old your children are other than one is 10. You need to ensure that you can keep all your luggage and children under control. If the youngest is 10, they should be able to manage their own luggage, but if the eldest is 10, they probably won't be able to.

With younger children, I think you would get a better experience if you moved around less, so I would have a week each in Rome, Paris and London and have day trips out from each. These cities are varied and your children will find the language in London easier to cope with (assuming they aren't bilingual).

Venice is a great city, but it's eye waveringly expensive and a 10 year old is unlikely to fully appreciate it, so head there when they are older.