This is unfortunately one of the many 'quirks' of default FSX; when winds aloft change there is no smoothing between the winds, therefore when the winds change, rather than a smooth transition you get shunted one way or another causing your aircraft to become either a missile or a dive bomber.
If you're able to, try using REX again. To keep your performance up set REX to the lowest options you seem fit and switch on the weather/wind smoothing option (It is called something similar). That way you can keep your performance and also have smooth weather transitions.
B)
*Edit - Apologies, I meant to explain that the weather smoothing will gradually change the winds aloft rather than shunt you, solving the problem.