is this the code that turns to follow path?
im not sure ,pretty new to using the car physics but thought i would
answer because this would be intresting to get into ...

max_angle = max_angle * (1 - (0.25 * time_step));
if (abs(max_angle) < 1)
max_angle = 0;
phcon_setparams2 (constr_front_left, vector (max_angle, max_angle, 0), nullvector, vector (95000, 500, 0));
phcon_setparams2 (constr_front_right, vector (max_angle, max_angle, 0), nullvector, vector (95000, 500, 0));
}

not tested or attempted to do this but does this code not hamper your
other turning code

stear_contr = (key_d - key_a);
max_angle += stear_contr * 10 * time_step;
max_angle = clamp (max_angle, -30, 30);

which perhaps results in
max_angle+=0*10*time_step;