If you book your next cruise while you are onboard, you get onboard credit, 10% discount (as long as the cruise isn't during a blackout date and a reduced deposit. You can put a deposit down for a "placeholder" if you haven't decided which cruise you want to take. Again, you have to do this ONBOARD while you are cruising. You can't call after your cruise has ended and get these perks applied to a new booking.
We did the Northern Europe B2B on the Magic with our DS, who was then 7, last summer (9 nights Norway, 11 nights Norway, Iceland, Scotland). It was AMAZING! We kept most of our excursions as half days, with the rest of the day poking around the ports, eating lunch, etc. Iceland was really the most intensive (the Golden Circle tour, which cannot be missed, was 8 hours long).
Is it doable with kids? Absolutely! My DS loved coming back from our tours and unwinding in the kids club!! That being said, I don't know if I would have done this as our first cruise. We had done a few Bahamas cruises, Bermuda and Alaska, prior to this one and I think it really prepared us for the cruise portion of the Europe cruise. We had also flown internationally the year before (for an ABD) and, I think, it was just last summer that I felt comfortable putting all of those components together - knowing how to pack efficiently, how to deal with the jet lag, knowing which excursions would work for us (I booked a lot of things privately), etc.
That being said, if you decide to do it, you will get a lot of your questions answered right here!!

I would suggest looking on cruisecritic.com as well for really useful advice particularly regarding port activities.
If you are going to do your first family cruise, to Europe no less, IMHO,
DCL is definitely the way to go.