I honestly think there's a little over-reaction here because the precise circumstances are unknown -- Big dog, little dog, dog that will sit quietly vs. one which is always on the move, etc.
As has already been mentioned, there is no specific law against driving with an animal on your lap; it could only come under driving without due care & attention, not being in proper control of the car, or something similar.
I did describe the officer and the two policeman that were helping me said a last name and rolled their eyes?
Every area seems to have one. When the other officers say something like "Oh yes, he's known for his 'zealous' approach," it probably means this is the umpteenth tale they've heard and they are as fed up with him as everybody else.
We had a W.P.C. working the little town near here a couple of summers ago who behaved the same way. I was driving about 15 m.p.h. through the High St., windows down as it was a warm summer day. I actually saw her glaring at me as I approached and then she quite literally shouted at me in the same manner as you describe. I'm sure regulars will guess
why, but the way she was behaving you'd think I'd just come running out of the bank with a gun and a mask and she was shouting "Stop thief!"
The way she was almost screaming across the street at me, I very nearly stopped the car right there and asked her who the heck she thought she was, but discretion got the better of me and I just kept going.
I found out later that she'd been going around the town like a nazi-stormtrooper all day and riled just about everybody over one thing or another.