I have checked, to such degree as I can, and it seems that you can have an illegally parked car towed away. The tow truck driver will want to take the car to an impound lot of some sort, because that is what they do.

If you want to "tow the offending vehicle out of the way a bit to create a space to get out", you can do that yourself, either by pushing, putting dollies under the wheels, or, if the car is small enough and you have enough help, lifting and carrying it.

I, along with Bruce, am completely flummoxed by your seeming inability to act in this situation. A sick woman was inconvenienced for three hours because no one was willing to cause inconvenience to an unknown person who had no hesitation to cause inconvenience to you.

You might want to think on that.