Having done a 3 week road trip with teens, and currently planning another 3 week trip for 6 (including my sister and brother in law), I’ll share my experience.
I think three areas in 28 days is fine. But you really need to focus on reducing your travel from place to place during that time. This will be most challenging in the Scotland/England leg. I would limit those 11 days to 2-3 locations (London, Edinburgh, somewhere in the highlands?)
Fly into one city (maybe Vienna?) and out of another (London/Edinburgh). Don’t waste time and $ backtracking.
As mentioned, don’t rent in one country and drop off in another. The price of minivan rentals is insane right now, so don’t be surprised. Limit the number of days you have the rental. Use trains as much as possible, and just rent when absolutely necessary. The ONLY way to get all of you in one vehicle is if everyone brings one carryon suitcase only, and maybe a day bag. I wouldn’t want to deal with two cars. Look at a minivan when you need a rental. Or if you don’t need it to transport luggage (just day trips), look at a small SUV or estate car.
Plan your lodging carefully. Apartments or multiple hotel rooms will be the only way to go. Decide if sofa beds are ok for your kids or sister. Many apartments consider a sofa bed in the living room a “bedroom” so if you want 3 actual bedrooms, you may need to search for 4 bedroom units. Very difficult to find.
Plan one “must see” per day. Don’t over fill your days or you’ll just be dragging grumpy people around. Talk about expectations in advance. Do you want to sleep in until 10, or do you want to be out the door by 8 am to beat the crowds? You’ll need to coordinate showers and be prepared for limited hot water! Some shower at night, some in the morning.
Plan for some down time. We do our “must see” in the morning, have a nice lunch (preferably someplace with a great view), return to the apartment for a break in afternoon (nap, laundry, teens check in with friends), then go back out in the evening. Remember dinner is later there, after 8pm some places.
Every time you move locations, you lose at least half a day. Limit your location changes. A travel day is the opposite of a rest day. Don’t count them in the same category, definitely leave “free days” about every 5 days. It also allows for some flexibility if weather doesn’t cooperate.
Your goal should be to create great memories and still get along after an extended period together! Don’t just tick off boxes of places to see. Be sure to include things of interest to the kids. My teens were done with churches and museums after the second of each. So we did sommerrodelbahns, a cave, a salt mine, paragliding, rowed a boat on lake Bled, visited WWII sites (oldest son’s interest). Each of them picked an item to collect (keychains, etc) from the various cities, so that was very fun for them to “hunt” for in various shops.