RPM drops and black smoke

Hello
I am an amateur when it comes to cars.
I'm having a weird problem with my car. Hopefully somebody could help.
When the engine is hot (above eighty degree) and when I hit the brakes and the car is almost at full stop the rpm's have a huge drop, the car shakes violently and it looks as the engine is stopping and also a lot of black smoke comes of the exhaust pipe. This happen for four to five seconds and then the car runs normally. Also, I have noticed that when the gear is in "drive" mode and I am holding the brakes black smoke comes out. Black smoke pops out even when I am driving in reverse. In "parking' mode no black smoke comes out and the engine runs smoothly. This problem happen only when the engine is hot. When the engine is cold (below eighty degree) there is no black smoke and no rpm's dropping. If anyone has any idea what is causing the problem I would be very obliged.
Thank you