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That should definitely work. Along with other things you've told us, I'd say that there is something wrong with your car.
Wasn't the boot already unlocked after you pressed unlock twice? It should have unnecessary to also press the boot button.
But it does. Page 20 step 8 describes the options for the unlock button. The second option causes a single press to "unlock the entire vehicle"...
RTFM page 19+: http://www.motoringalliance.com/pdf/manuals/2009_MINI_Hardtop.pdf
The middle button is to turn off auto start/stop, which was in European R56 but MINI didn't bring to the US. [IMG]
The Sport button is included as standard for an S in the US, but it is an extra cost option in most parts of the world depending on country.
F1 Explained: What makes the perfect pit stop? - YouTube
This is the same as the BMW X1, 3rd gen Clubman and 2017 Countryman (same UKL platform), but with a sedan body. Just swap in the front bumper and...
He's just a normal BMW driver.