Yes practice braking, even if it’s green. It’s arguably the hardest think in Karting.
You need to attack. If the motor is shutting down, you’ll probably need a carb adjustment too.
Maybe we can have a brake-off at Stockholm when it warms up 
Also, worth listening to the podcast series we did with Mr @Terence_Dove on driving techniques if you haven’t already. It’s on SoundCloud and iTunes.
Episode 20: (Part 1) "Learn How to Master the Art of Kart Driving" with Terence Dove