When going on the brake it jerks to the right side

2015 Juke. Once the motor/transmission gets warm and I stop using the accelerator, the car jerks, motor struggles & shuts off. It won't start again until it's completely cooled off. If stopping at a stop sign or red light, using thr brake & accelerator (keeping the RPMs up), the motor does not shut off. I was told it might be a transmission problem? But why would the transmission make the motor act as if it's starving for gas?