Maybe you should narrow the choices down a little? Rome and Venice are very far from Amsterdam or London. You could feasibly do this, but you'd honestly be on a train or plane for more than you'd be in the cities enjoying yourselves. Why not just keep it to London, Paris and Amsterdam and then you can have 3 days in each city, plus travel time between. Going down to Venice or Rome is time consuming unless you plan on flying to and from.
Sample itinerary: Fly into London, see the city and surrounding areas for 3 days then take the high-speed train to Paris (90 minutes) and see Paris for 3 days, including perhaps a day trip to Versailles. Next, take a train to Amsterdam, which I think is around 4 hours, normal speed. You can then spend your last few days in Amsterdam and chill out for the flight back to Texas. Remember, you lose a day traveling when you come over from USA, so you have less than 2 weeks, travel time included.
Last tip: look into buying a Eurail ticket, if you are under 25 years old. You can use that for your train tickets and go anywhere you want via train, all over Europe! Get it before you come over!