This is madness. You will die (or you will want to). You're planning to put your kids through this? Prepare for a lifetime of therapy...
OK, stop, put down whatever you're consuming. Start over. Begin by sharing what your actual arrival and departure dates are, and where you're flying in from. If that's from far away (like North America or other place similarly distant), don't count your arrival or departure days, because you and/or at least one member of your group will be exhausted, cranky, jetlagged, and only interested in going to sleep on your arrival day. You should try to stay awake until after (early) dinner that day, but otherwise write it off as a usable day. Same with departure day. OK, so how many full days in Europe does that leave you? Then consider that every time you pick up and move to a new location, that will consume pretty much the whole day. If you're flying someplace, that whole day is used. If you are taking a train from city-center-to-city-center, and if you are all efficient, experienced travelers, then that's going to take 1/2 day (at best) but usually more like 3/4 of a day. So subtract each relocation day. How many full days are you left with? When you do the math like that - and when you're honest with yourself - you can see how your usable days quickly dwindle.
I'm guessing that, not including arrival/departure days, you will have around 20 full days. With that, I'd suggest you can do this two ways: A) Pick one country - Italy or Spain, not both - and go to all the places you want to see (on your preliminary list); or B) Do a portion of both countries, but not all of what you list.
Keep the following in mind:
1) You will have kids in tow. Kids generally are not "road warriors" who get up at the crack of dawn and go go go through museums, trains, strange food, and all the other things one goes through on foreign adventure, quickly and efficiently, good-naturedly toughing it out at every challenge. You will need to calibrate your expectations for the little ones. Are they ever picky, demanding, moody? Calibrate again.
2) Any group only moves as fast (or slowly) and as efficiently (or not) as it's slowest/grumpiest member. That might be one of your kids or it might be an adult. In any case, you need to take that into account.
Bottom line: your initial proposal looks unrealistic to me. IMHO you need to dial it down significantly just to be able to pull it off at all, to make it enjoyable for all (and not to turn your kids off from traveling with you ever again) I'd suggest you slow it down a lot and focus on fewer places so you can enjoy it.
Personally, I'd pick either Spain or Italy, not both. Either offers way more than you could possibly do in 20 days.
Good luck.