[Kevan]

Try testing with the body off to see if there's any bad tyre to body interference. 

Is there backlash in the gearmesh, a tight gearmesh can cause super fast braking and inlines kick sideways under severe braking. 

Are both wheels firmly fixed to the rear axle and both tyres firmly on the rear wheels and not slipping round.
Are both rear bearings firmly fixed in the chassis. 

If all else fails turn the brakes down.