Our dog was for us one of the reasons to buy the M3W. We're bike riders since young but on a bike one can't take a dog.
We first try two persons and our dog (Labrador) in one M3W but that was really cramped (special for the dog)
In that mean time we loved the M3W so much that the only way to do was order a second M3W.
This is what we did. Need to say that our dog is very calm, thats something whats necessary to take a dog in a M3W.
We trained her by going for a swim (she likes to swim very much) every time we went for a ride. So she quickly made the connection M3W and swimming.
We don't have her on a lash or attached to the car. Don't know if this will be better, it's also depending on the dog.
When it starts raining we put half of the cover on the car so she stay dry.
The only thing what she (AND WE) don't like is the screaming sound of the bevel box. But hopefully in the future there will be a solution to that,

If it's legal or illegal I don't know, will be different in every country. But if the police stops you they also don't know because they don't know where to place the M3W.
Is it a car ? Is it a bike? So do like the Chinees, smile, smile, Say yes yes yes. Say sorry sorry. And do if you don't understand what they talking about.
Good change that they let you go.