Lots of good questions
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Budapest, Vienna, and Prague all deserve at least 3 days each in my opinion. Assuming you'll want to spend a couple days in Copenhagen before your cruise, and add in some travel time, you have only a day or two for side trips to places like Cesky Krumlov. If you're set on visiting those 3 big cities (they are 3 of the best, and well worth it) then I wouldn't build in more than one extra stop.
SOME trains are inexpensive. Sometimes you'll find it's cheaper and faster to fly. I'd suggest you look into flying from Prague to Copenhagen. For Budapest to Vienna, the train is definitely the way to go. Vienna to Cesky Krumlov/Prague, I'd explore trains and buses to start with.
I'm with your husband on the car rental. Sometimes it's necessary, but the trains are so simple and convenient, even to get to most small towns, and parking can often be difficult or expensive for a car.
As far as language goes, I speak English, a little Spanish, and a little French. I've never had a problem in Europe. In all the places you've listed, and any tourist-heavy area English will be fairly prevalent, and you'll have no problems. I always try to learn a few words like hello, please, thank you. I don't know if people care, but it makes me feel better
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Given that you're having some trouble planning, here's my suggestion...start by planning those big cities you listed. Look up what you want to do and see in each one, and figure out how long it will take you to travel between them That will give you a rough itinerary. Then if you have some extra time, research side trips like Cesky Krumlov (or my highly recommended Melk, a short train ride from Vienna). If there's a side trip you're dying to make, you can make a call on whether to skip a big city or shorten one by a day if it doesn't fit.
Hope that helps get you started. People here are generally very helpful providing feedback on an itinerary if you can pull together a first draft and want to test it.