As was said, the US v UK for PPL debate has been well-rehearsed here and for decades !. .It attracts, also, the ('email me') recruiters.. .I am not recommending anywhere but these points may assist.
If you can't devote 3 or 4 weeks to a course and have plenty of money, learning in the U.K. is the only way, despite the weather and other problems.
In my experience, most people who have a problem would have it anywhere, although being in a different country/culture might make it worse. In any case, gaining a PPL in 3 weeks will, obviously, require reasonable ability, high commitment and plenty of effort. Even with good preparation, it isn't going to be a holiday, although you may be in Florida or California, so just forget bars, the beach and any bonking until you've passed.
I'm sure it's true that a few do it in 2 weeks or less but, if you have the time, wouldn't the school allow you to take longer than 3 or, even, 4 weeks as it would only require booking (and paying for) extra accommodation?
I believe you would need plenty of time or have to be very clever to perform properly on a combined PPL course/family holiday.
Ham said - "some" US schools will expect you to commit yourself 100% to the course. Unless you are paying by the hour (in which case they don't care how much you spend !) wouldn't any school anywhere expect you to be 100% commited to their course?