Personally I have not had any issues with my wingmen like the one you describe. I am running EEAH/EECH version 1.14.1.
The bleeps and chopper movement sounds like one of a few possible problems:
1. Too much torque - anything over 100% and your engines will start to overheat before popping
2. Too much airspeed - go too fast and you'll rip your rotors off. "Too fast" depends on the chopper, but it tends to be around 170-180+. Just keep your eye on your speed and if your chopper starts acting funny...slow down a bit.
3. Turning too fast/banking too hard - not sure what happens technically speaking, but have noticed the chopper getting all shakey when banking too hard, easing off sorts it.
I could be wrong of course -- maybe it's your maniacal wingmen buzzing the newbie. It just might be worth checking that it's not any of the above though.
If you haven't done so already, I'd check out these guides by Beach:
Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4 Hope this helps. Good luck!