Checking Tires, wheels, mounting systems, steering head bearings, swingarm bushings or things as simple as playing with tire pressures can alleviate a low speed headshake. Not always though as sometimes a damper is required.
Jack up the sidecar wheel and see if you have any runout when you spin it. Also check for loose spokes.
I think the 'Bimmer' is marketed by Tran Moto and is based on a Chang Jaing chassis. I would suggest you contact Trans Moto. I do not know what they do as far as mounts go nor if they utilize a different than stock sidecar wheel.