Train vs Plane Flights for family of 5 - London, Germany, Italy summer 2018

I cannot help with BMI, but from Germany into Italy is easy and inexpensive by train, starting in Munich and heading to a first stop in northern Italy. Then work your way south through Italy.

For tickets bought 5 months in advance I found Sparangebot tickets for €29,90 for Munich to Bolzano (4 hours 15 minutes); € 39,90 if you stay on the train till Verona (5 hours 45 minutes). Those are direct trains with no changes, city center to city center. No airport transfer fees, no waiting in security lines, no worries about baggage size or weight, no extra charge for seat reservations.

You say you need to make hops from London to Germany but then mention Bristol airport so its not clear where your starting point is. If it’s the Cotswolds then Birmingham airport may be convenient – otherwise Heathrow isn’t too far though it’s not an airport for the low cost airlines.

As for BMI, well they will be safe planes that will get you there…

Have you considered a car lease? Flights or trains are good for direct city to city legs, but not very good if you want to make a stop or two on the way. Some comments on that below. Otherwise, For me it's a leg by leg question. For many longer legs a plane is both quicker and cheaper than train options (note: I now travel with a only a carry-on bag that fits even Ryan Air's limited allowance but it seems to be true for non-budget airlines too). For me, if the flight is an hour or more, it's probably the better choice. If the train is two hours or less, I'd go with the train. In between, you have to weight the options but an hour on a plane can replace more than five hours on a train. Trains can be a very affordable option when you buy well in advance. You lose flexibility, however, if you miss the train you have to replace the ticket at full price.

I took five of us for a trip from Amsterdam to Rome (via Germany and Austria). The car lease was a really good deal, better than train, plane or car rental. They charged a fee for pick up and drop off but it was reasonable, 100 euro to pick up in A-dam and 150 to drop in Rome. The lease includes full CDW in the price, unlike a rental.

Since then I've started using American Express CDW on my car rentals and it's worth considering if you might rent. I've decided (maybe not correctly) that rentals are better on basic economy models. As you go up in size or quality, rentals go up quickly, making a lease the better option for longer drives. For five of us, a seven passenger Grand Scenic II was just about right. It had enough space to seat everyone comfortably and hold our one carry-on each. If we were bigger or had more baggage, we would have wanted something even larger.

With three weeks and that many destinations, driving wouldn't be the optimal choice - it simply takes too long to get from Point A to Point B .
Since time will be of the essence in order to see everything you have listed, I would look at the estimated train travel time between destinations and compare that to flights - factoring in that most airports are located outside of city centers (unlike the trains) and you will need to arrive about 2 hours before your flight to clear security, etc., etc. So, even though a flight might be two hours versus 6 hours for the train, by the time you factor in travel to the airport, time for security and travel from the airport to your new lodgings, you may be better off taking the train.
One thing to bear in mind is that with travel, it is always a trade off between time and money!

Wow! Thank you so much for the helpful tips already. We're flying into Heathrow mid July and out of Venice 3 1/2 weeks later. (Award travel so we are working around what was available.) We are meeting up with friends in Rothenburg mid trip so that also guides our itinerary. Limited budget (but setting $ aside of course for museum/church/castle admission, a few special meals and lots of gelato!)
I was considering making our hop from Bristol because it's a hub for BMI to Germany and we will be in that region outside of London, but was just searching for good deals really. I just don't want to get burned with an airline cancelling our flight or paying stiff fees and it seems like it would eat up a lot of time doing the train for that UK to Germany HOP.

Tentative itinerary including many highlights my husband & I have already visited, just now with our 3 kids -- PDX to Heathrow. London 4-5 days, will get rental car, stay in airbnb for 4-5 nights and make a few stops from this list: Stratford upon Avon, Warwick, Cotswolds, Bourton on water, Oxford, Bath.

HOP (by plane or train) to Munich or Frankfurt and spend one week max in Germany- connecting with friends in Rothenburg and for rest of time choosing from this list: Neuschwanstein, Rhine River castle towns, possibly take teens to Dachau,
HOP to Rome and work our way back up Italy for one week, probably by train through Florence, departing Venice. We spent a lot of time before in Italy so will have a difficult time narrowing it down and picking highlights good for the family.

Right now I'm trying to get the two HOPS worked out so I can also fill in the other lodging and car rental etc.
BRAD- Thank you for the tip on car "lease" I will look into that-- what companies do you reccommend?

What are the ages of the family members? You can travel pretty cheap in Germany by regional train.