Car shuts off

When driving and start to slowdown car starts to
pulsate the longer I am at a stop light it pulsate
heavier and on occasion it shuts off, while driving
at a normal speed do not have the heavy pulsation
nor shutting off, what could it be, motor mounts,
serpentine belt, front and back brakes was
replaced, the problem is still there, engine light is
on the dashboard code refer to an evap control
system, large leak, please I will appreciate if
someone could come up with an answer, so far
different mechanic cannot hit with the problem,
and I keep spending and the problem is not getting
solve.