Will you have access to a car during your stay in Amsterdam?
If so there are plenty of places you can visit within the Netherlands during your stay there - think about Friesland, Drenthe, Overijssel, Groningen, the Wadden Islands.
Even without a car you can get to many lovely, not so touristy places by train. But I am sure your Ma-in-law knows all those places.

The easiest way to get to Paris is by train - you need to book your Thalys tickets as early as possible to get a good price.

Thank you hetismij2 for your advice! Yes we have a car access while staying in Netherlands.. Would take that for Paris and will see also some options for train tickets as I saw a Eurail pass tickets allowing travel from two countries depending on how many days you want.. Thank you very much!

Do not assume a Eurail pass will save you money. Cheap tickets are available point to point in all the countries you are interested in visiting, especially if you buy them on line in advance. And I would never drive to Paris and plan on having a car there; parking is scarce and costs a fortune, and you will have absolutely no need for a car in the city.

You should also look into cheap flights (www.whichbudget.com) between countries, especially for getting between France and Italy, as train connections between the two can be problematic logistically.

The car access that I meant was for Netherlands Noted for that, I checked on the link and it's interesting! Will do more planning then, thank you StCirq

Just a quick thought, it may be less expensive to travel from Amsterdam to Paris on the train via Germany. Thalys appears to have a real monopoly on the Amsterdam/Brussels/Paris direct route...