If you're getting blur on moving objects that means the shutter speed is too long.
The "night" exposure mode allows the shutter speed to ramp up more freely than the default "auto" mode but it should still be limited by framerate (in other words shutter speed can never be longer than 1/framerate, so if framerate is 30fps then shutter speed shouldn't be able to exceed 33.333ms).
You can certainly fix the shutter speed with the
-ss option which will eliminate the blurring (assuming you set it fast enough), but don't be surprised if the scene comes back too dark. If the camera is ramping up the shutter speed, I'd assume it's already maxed out the sensor gain, has "decided" the scene is still too dark, and is attempting to compensate with longer exposures.
For that matter, it may be worth checking the camera gains with the raspivid
-set option (this dumps shutter speed, analog gain, digital gain, and AWB red/blue gains to the console repeatedly while recording). The maximum gains are 8.0 for both analog and digital. If the analog gain has maxed out, and the shutter speed is still ramping up then you simply need more illumination.