Hi jutiner,
You don't say when you are traveling. There is so much to consider in making the various decisions. First, budget: trains and flights have different prices. Same with Airbnb vs. hotels. Then, time. I am also traveling with three kids to three countries for 34 nights and here's how I thought about it:
We are flying in and out of Paris because it was the cheapest of all the flights I could find (and for 5 people, budget is very important). We rented a car for our time in France (after Paris) because trains were more expensive for 5 people than a rental car, AND, our destinations were not as easily accessible by train - so we would be spending a lot of time on travel, rather than being there. We leave the car in Nice, and take trains into Italy for our next part of the trip. In Italy we have 3 locations: Cinque Terra, Florence, and Rome, and we train the whole time (because each destination is well served by trains, and Italian trains have something called Bimbi gratis which means our kids ride free ... and we prefer trains anyway). We fly from Rome to Amsterdam, which cost WAY less than a train and takes WAY less time. And then we train from Amsterdam back to Paris at the end, although in this case, I did find flights for the same price, but again, we prefer trains.
We are staying primarily in airbnb's (which I studied assiduously: read all reviews, verified hosts, etc) throughout our trip, except for a few b&b's, again, because for 5, airbnb is cheaper. The upside to airbnb's can be price - depends on what you select for a place - and access to a kitchen (again, you have to study each listing for amenities, and look at the pictures to see what they look like - hot plate or stove top, etc) so you can stay in some nights and cook if you want, and eat breakfasts in. Saves a lot on food, and eating out very soon starts to be work. The downside is that they are less vacation-y, as in, I am looking forward to the b& b's where I wake up and there is a spread of breakfast, and everything is taken care of. We are doing both and I have done both before, and enjoyed both options for different reasons.
So, you would have to check if high speed trains follow all the routes you want to travel, look at how much time/money you will spend compared to rental car compared to flight. I would make a list of the specific places you want to visit, put them in an order that makes sense, and start looking at transportation options/costs/time. Then I would look at places to stay and compare what you get. Finding one hotel room for 5 can be a challenge, and expensive - depends where you are going. After all that, you start fine tuning your visit to each place by looking at sites - open/closing times/days, prices, how to buy tickets. The you start buying tickets for those things you want. And so on.
It is a lot of work. There's not really a way to avoid it (although I find it SO fun - the planning) - unless you hired someone to do it all, but planning is half the fun.
Just think that the more work you do up front, the more amazing your trip will be, and for this much money, it should be pretty well planned, don't you think
cheers,
Jessica