If alpha_dot is going very large, you could consider filtering or smoothing out the large jumps.
Alternatively or additionally you can insert a gain block: alpha_dot = k*lateralAcceleration/v where k is a proportional gain that you can tune such that alpha_dot is within an acceptable range.
After you integrate alpha_dot to get alpha you need to wrap it between -pi and pi or 0 and 2 pi, whatever convention you are using, using mod, e.g.
angle_wrapped = ( mod( (angle-angle_min),(angle_max-angle_min)) +angle_min);
I don't remember if Simulink already has a wrap block, but there is already a wrapToPi function in the mapping toolbox if you have that.