Please help us plan summer vacation

I'm UK biased ..... :) so I'd say Alton Towers for sure. In June you will need 1-2 days. I didn't think Derren's Brown ghost train was worth the wait to be honest, although with all the screaming going on around me I'm sure some people thought it was good !! As I've said before, The Swarm at Thorpe park is the worth the price of the admission ticket. I'd ride The Swarm any day over The Gatekeeper at CP.
Good luck with planning your vacation, I always find that as much fun as going to the parks.

My son and I really enjoyed The Void (DSTP). We think it is second only to "Flight of Passage" (DAK) at Walt Disney World.

How will you reach Venice if your wishlist is mainly London attractions? You need an extra 2 days of travel to get down to Rome and Venice. You should just stick to London.

I would do two days at Europa, one day at Efteling. I would add Toverland and Phantasialand. Drop Alton Towers and Thorpe park. Phantasialand is a little over 2 hours from Efteling and Toverland is in between the two parks. Both are great parks.

I love Alton Towers and Thorpe however if your at Efteling it's so easy and quick to visit Toverland and Phantasialand.

...or just do London and Paris. 10 days is not much time considering you're losing almost a full day on either end of your trip for trans-Atlantic travel (assuming you're coming from North America). You'll lose another half day just going between London and Paris.

Honestly, I think if this is your first trip to Europe, you should limit yourself to just one or two days dedicated to theme parks. I know it's tempting to want to see as many as you can as Europe offers so many unique parks in relatively close proximity, but there are far more interesting places to visit outside of the parks. You could easily spend a week in London and/or Paris and not even scratch the surface of iconic and culturally significant sites (Tower of London, British Museum - I could easily spend 2 days just in here, Buckingham Palace, Westminster Abbey, Louvre, Eiffel Tower, Notre Dame, etc...). There's something to be said for going against the grain and deliberately avoiding the most popular sites, but the way I look at it, you might never go back to these landmark cities. Do you want to spend a bulk of your limited vacation time riding a handful of unique rides and dozens of clones and similar rides you could experience closer to home OR see iconic places you may never have a chance to see again? It's one thing if you're one of the coaster counters that obsess over how many different roller coasters they've ridden around the world, or if you want to plan a trip solely dedicated to experiencing European theme parks. However, it sounds like you and your sister are more interested in the full European tour experience, which will be difficult in 10 days if you're spending 4-6 of those days in theme parks (along with spending a lot on admission and transportation to those parks as well).

My wife and I went to Europe 6 years ago for a 10-day trip across 4 cities (Prague, Stockholm, Gothenburg, and Copenhagen), and could only find time for a little more than a half-day to spend at Tivoli (we did spend almost a full day at Skansen, which perhaps in TH's warped world is a theme park too). We thought about going to Liseburg, but it was closed for the season when we were there, which would still only have been 2 theme park days out of our 10-day vacation. If we ever do go back to Scandinavia and Central Europe, a couple of theme park days would probably be on the itinerary, but they would likely never exceed more than 20% of our total vacation days.

I wholeheartedly agree with Russell here - as much as I love places like Futuroscope and Europa Park, they just aren't worth sacrificing time for when you're only visiting for 10 days. And there isn't a single park on your list that demands more than one day, particularly on such a tight itinerary. Yes, you might not hit every single attraction, but you'd absolutely manage the headliners.

We have such a rich cultural history in European cities that the real value is in taking your time to explore them, rather than just ticking off the tourist headliners. Get that selfie on top of the Eiffel Tower or in front of the Colosseum, sure, but giving yourself a few days to get under the skin of Paris' Belleville district or Trastevere in Rome (for instance) is just as valuable.

I tend to be a bit blasé about London given I've lived here for a lot of my life - the city is becoming a rich person's playground dotted with tourist traps, and the cultural hotspots outside the centre probably hold little interest to first-time tourists. But it is undeniably a good travel combo with Paris - and the Eurostar means you won't waste as much valuable time travelling, as others have suggested. (A flight from one country to another will kill at least half your day.) Also, parks like Efteling, Futuroscope and Europa are real pains to get to using public transport.

If however you do decide to do a hopping trip of the cities you mentioned, there is a time-efficient (and, assuming you book enough in advance, fairly cost-efficient) way of achieving this with trains. London to Paris is an easy Eurostar journey. There's a direct Paris to Venice sleeper train (with the added benefit of saving you a night's hotel cost, of course) and once you're in Italy, you can get from city to city in a few hours.

Honestly, as fun as the Leaning Tower looks, the rest of Pisa is pretty unremarkable, so I'd skip it this time around - particularly if you've already got Venice and Rome on your itinerary. (Venice too is a bit of a disappointment once you've seen the centre, so don't plan to spend more than a day there.)

€100 is more than enough for food and travel within a city, yes.

If you're really set on squeezing Efteling in - and honestly, I can't blame you - then maybe add Amsterdam on to London and/or Paris. Now that Eurostar are running direct services, it's a lot more feasible. (Getting to the park from Amsterdam is still a hassle though, requiring two trains and a bus.) But seriously, one day is enough when you're this tight for time.

So yes, in conclusion: London/Paris/Amsterdam would be rushed, but not unrealistic. Adding Italy into the mix however would just mean you won't have time to appreciate anything other than taking a photos in front of a few famous buildings before moving onto the next city - and where's the fun in that? Save it for the next time you visit Europe. (Or, you know, turn this trip into Rome/Venice/Barcelona...)

Finally: I wouldn't recommend giving up any of your time in the UK to theme parks. Alton Towers is great, but would be such a huge block of your time with travelling (unless you were already planning to be in a Midlands or Nothern city) that it simply isn't worth the sacrifice. DBGT (which is at Thorpe, yes) is a fascinating (albeit only somewhat-successful) experiment into what the future of theme park attractions might be, but definitely isn't worth sacrificing a day elsewhere for. The rest of the park is fine, but unremarkable if you've been to any mid-level amusement park in the US.

Alton towers is great, but it is awkward to get to.

Another option for you might be Blackpool Pleasure Beach. You will need to have a day to get there/back from London (trains are best). I wouldn’t call it a theme park, but rather an amusement park. It does have several world class rides and a few classic woodies.

Also look out for the dungeons, there’s one in London and Blackpool as well as other locations. Overpriced? Probably, but still a good experience that you can fit in an hour or two.