If your getting hypo symptoms at 3.9 & below then that's normal, your concern would be if you weren't getting any at all.
As for getting another Dr to prescribe the insulin, that wouldn't be a good idea even if they could, if your gp has little knowledge of diabetes and how insulin works then you should ask them to refer you over to the care of the hospital diabetes clinic, they are more experienced at dealing with issues relating to insulin.
To stop your bg dropping over night you need to reduce your levemir dose, start off by reducing it by one unit and test and see how you get on, if need be reduce it again.
btw, are you a type 1 or type 2?