travel destinations between london and rome and transport ??

I highly recommend that you read this information from the Man in Seat 61 regarding train travel in Europe:

http://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#Should you buy a railpass or pay-as-you-go

Do not assume that a rail pass is your best option - most likely it is not.

That's exactly the problem. I had seen this and many other posts too but its still damn confusing whether for my itinerary what should be my mode of transport and if train then whether I should take a eurail pass or swiss pass or nothing.

To start, I would add a couple more days each to Paris and London.

I do not know why you need to spend so much time in Switzerland whereas you spend so little time in Italy. 3 days in Switzerland is enough.
If you come from London, I would take the Eurostar to Paris then take the thello train by night from Paris to Venice ( you may also decide to stop in Verona, town of Romeo and Giulietta) and from Venice you have direct fast train to Florence and Rome ( need at least 4 full days in Rome, 3 in Venice and 3 in Florence)
You may as well take the TGV from Paris to Milan.
Make sure you specify you are a family when travelling on European trains.

I am seriously thinking of adding Norway to my pla.
So it could be
London 3
Edinburgh 2
Norway 4
hamburg/Amsterdam 2
Paris 4
Switzerland 5
Venice 2
Florence 2
Rome 4

Pls suggest

I suggest you plot the cities on a map. You have hamburg and Amsterdam combined, with a total of 2 days allowed to travel to and visit both. If you mean Hamburg Germany, it is hundreds of kilometers from Amsterdam. Even if you fly between them, you're not going to have time to visit either city.

Also, I suggest you calculate the travel time between cities because I don't see that you're allowing enough travel time. You will lose one-half day to a full day of touring every time you change cities. With the number of places you want to go, you will see mostly the inside of trains, planes, airports, and train stations. But obviously, travel preferences differ.

I actually meant either amsterdam or hamburg.

I am getting inclined towards the following plan

london (3) - edinburg + isle or skye (2) - norway (4) - amsterdam (2) - paris (3) - switzerland (7) - venice (2) - Siena (1) - Rome (4)

Pls suggest modifications to it and transport plan.

OK, this is some useful detail that was missing from your several other questions. But it's clearly not yet a firm plan. Please read carefully my answer about rail passes. Both kids will be free with any rail pass, or will usually pay half price for point-to-point train tickets. You cannot make any meaningful rail pass comparison until you make some more trip decisions. At the very least, try to narrow down the countries. If I had 4 weeks to spend in Britain, France, Switzerland, and Italy, I would not add any other countries.

Is there any significant factor that will prevent you from making some firm reservations and purchases soon? For instance, have you already received the visas?

No visas or hotel or transport bookings yet. Only the main flights I have booked. From the plan I just wrote above I can remove Amsterdam and all a place maybe in Italy.

With kids along, we are more into nature than art and architecture. Why do I need more that 2-3 days in London and Rome.

With kids, London is one of the best cities in the world. It easily justifies 4-5 days at a minimum

Natural History Museum
Churchill's war rooms
changing of the guard
Hampton Court, including the maze
The Tower of London
Greenwich
London Eye
watching a football match
Imperial War Museum
Science Museum
etc etc