Stalls while driving at random

I have a 2002 mercury grand marquis and recently while
driving  it will rumble and shut off. The battery and check
engine light will come on. I can turn the key off and it will
start right back and drive and may or may not do it again
for several days or it may do it 5 min later. Sometimes
when you press on the gas it will shake and the coolant
light will flash but it doesnt die.  Ive had it to 3 shops and 4
different mechanics and they can't figure out what is wrong
with it.