Since mines and LAW rockets cause explosions, I would use the Explosions
rules from the Spot Rules chapter and apply all the explosion damage as ge-
neral damage to vehicle and passengers alike.
The mine would detonate within 1 m of the car and would cause the 6d6+6
hit points damage, reducing your car to 9 hit points on average (let us not
mention the poor passenger ...).
Since your vehicle would still have more than 5 hit points, but less than half
of the hits points it started with, the Vehicle Damage rules on p. 216 / 217
would allow you to drive what remained of your vehicle at half speed, if you
wanted. Think of a vehicle that has been thrown through the air and badly
damaged by the mine blast, but is still able to crawl.
Later on the first LAW rocket would almost vaporize the wreck of the car with
28 points of damage against the remaining 9 hit points.
Well, at least this is how I would handle it.
Edit.:
On second thoughts, if you divide the car into hit locations, with a zone within
1 m of the mine explosion and a second zone within 1 + m from the explosion,
and give the lower zone - most probably including the engine or other vital
parts - 75 % of the weight and hit points of the car, this lower zone will take
enough damage to destroy the engine completely, I think.