Ok, then the courts decided that mom's visitation should be supervised because she is a potential risk to herself and the children. However, the courts did not feel that the risks were severe enough to require professional supervision or a specific supervisor, only that she needed to have another adult present. That is actually pretty "supervision lite".
Between this thread, and your other thread, you are not at all clear on what your goal is.
What your goal SHOULD be, is to ensure that the children can have an ongoing relationship with their mother in a way that is safe for the children and ensures that the children are not at risk.
Therefore yes, you should be filing for contempt, (and you shouldn't be so worried about what type of contempt) but more importantly you should also be filing to modify the orders so that mom is unable to play the games she has been playing with the supervision.
You should be filing to modify the orders so that either a specific supervisor is named who will take their duties seriously, or you should be filing to for professional supervision to be ordered. Are there any members of mom's family who agree that she is a risk and would be willing to be named supervisors and would take it seriously?
However, again, the kind of supervision ordered was about the lightest form of supervision that I have ever observed. Therefore there is a slight risk that a court could determine that mom no longer needed supervision.