It's very rushed but it's (almost) doable train-wise.

Mandatory seat reservations will be a significant part of your budget, have a look at https://www.seat61.com/interrail-and-eurail-reservations.htm

For example the Paris - Amsterdam Eurostar costs 32€ per person. You must book early as it's a popular route and there's a passholder quota.

You may take the Amsterdam - Basel/Zurich night train : book early, popular and capacity is limited. I'd go all the way to Zurich for a slightly longer night's sleep.

Swiss cities are forgettable. With so little time I'd concentrate on the Alps themselves. Eurail is fully valid on boats on Lake Thun and Brienz + the pass also gives discounts on (expensive) mountain peaks.

Day 6 is basically impossible. Instead take the Bernina Railway towards Venice and either go all the way or stop for the night on Lake Como (Varenna).

Do not use the panorama carriages, not worth it in my opinion : 36 CHF extra for full and loud carriages. Better to board the regular carriages at the front : reservation-free, less busy, pull-down windows = better experience.

Forget Pisa and go straight to Florence/Rome

Honestly I'd even skip another Italian city. You'll spend more time on trains than in the cities themselves!

EDIT : Public transportation within cities is not included except some suburban trains.

I know that your time is limited but you'll be exhausted the whole trip. Please on't plan too much, especially with a 2 y.o. child. You'll barely have half a day in Paris!

This was my personal advice, of course you can do whatever you want.

Appreciate your suggestions @thibcabe . Could you please suggest if any flight routes can be preferred over trains routes in terms of budget and time?

Flying takes time and is stressful too. You’re on a train travel forum so obviously we’re all a little biased. ;)

I’d rather cut a city or two to have a more pleasant experience.

In your itinerary, Amsterdam is somewhat out of your course.

By skipping it, you avoid expensive Nighttrain and Eurostar (red) reservations (which you will need to take, to keep up the high tempo if you still want to visit something). Skipping Amsterdam will free more space to enjoy the alps. Otherwise you’ll spend more time in trains, than effectively enjoying your stay somewhere.

But that’s only my opinion of course Less destinations, is always more experience.

How expensive are we talking for the night train interlac to Amsterdam . Is it work it for the experience?

Looks like price varies. please check here https://www.nightjet.com/en/ticket-buchen/#/home 

There is no night train from Interlaken, but you change to the night train in Basel. A seat reservation on the night train is €3; a couchette or a sleeper is more expensive and has dynamic prices, depending on demand. Also for pass reservations.