Skyy,, you are going to Europe for ten days.
You understand that when you stay in a place for two nights you have actually only allowed one full day there,, each time you move you will use AT LEAST half a day,, checking out of hotel, getting to train station or airport.. then the travel, then getting from train or airport to next hotel and checking in.. so leaving optimistically 1.5 days in a place.. so .. you want to visit say Rome,, and only have one full day there.. because the other full day you will leave the city early for a daytrip.
I suggest you edit. .. ten days is not enough time to do everything you want. I would beg borrow or steal to make it at least a 14 day long trip,, airfare is so expensive,, make it worthwhile coming over.
As Sarah said,, Viatour is not a tour company, they just sell tours. You can probably find same tours a bit cheaper yourselves.. and you are right, you do not need to prebook ... EXCEPT.. you have only allowed 2 days in most places and it is easy to find tours full. I was in Paris one summer and couldn't get a daytrip I wanted to take for three days.. unfortunately I was leaving in two days! The desk clerk tried helping me too.. we must have phoned like 4 or 5 companies.. Some daytrips do not run every day.. maybe every other day.. so its easy to find them full .. this would not be an issue if you weren;t on such a tight timeline, so since you are pretty sure of which are "must dos" I would work my trip a bit different .
You haven't mentioned when trip is.. but europe is pretty busy year round,, and when some of those places are a bit quieter ( like now till about April) the tour companies often just operate with less tours.. IF going in summer don't count on them having empty seats to fill.... If going off season you may hit it lucky.. but you are travelling thousands of miles and have said you really want to do these two daytrips.. wouldn't it be dissappointing to get that close and then not be able to go!
I think with ten days you should stick to three destinations.. especially with daytrips..
If you haven;t bought your air tickets yet be sure to buy open jaw or you will end up wasting a day getting back to departure air city..