marinee,
Your proposed Itinerary is possible, but keep in mind that you likely won't get as much touring done in Amsterdam as planned due to jet lag. I tend to agree with the previous reply that you might limit your stay to just Paris and London this time (10 days is not a long time), but your choice of course.
The trip from Amsterdam to Paris only takes about three hours via high speed Thalys (reservations compulsory), so you don't have to allot a full day for that. You could have a relaxing breakfast in Amsterdam and be in Paris for lunch. You'll have to be clear on which rail stations you're using in each city, as there are usually more than one (Paris has about six stations). On the Amsterdam - Paris route you'll likely be using Amsterdam Centraal and Paris Gare du Nord.
You can save considerably with pre-purchase of tickets on the EuroStar from Paris to London. Note that the cheap tickets are usually non-refundable and non-changeable, so choose carefully when you buy them. You'll need to check-in at the station at least 30 minutes prior to departure, or you won't be riding. You'll have to go through airport-style security on the EuroStar and will also clear U.K. Passport control in Paris, so leave lots of time. For full information on the EuroStar, have a look at the excellent Man In Seat 61 website. You'll need to do some research to determine how to get from London St. Pancras to the part of London where your hotel is located.
I also agree with the others that using open-jaw flights (ie: inbound Paris, outbound London) would be the best idea.
It would help to know whether either of you has travelled in Europe before?