There are ethical and psychological elements at play in this situation. When this situation occurs the parent and the child most likely have little trust for each other. The parent does not trust their child to remain pure. The child is rebellious and performing impure actions, at least in the eyes of the parent.
Parents who force or coerce young ones to wear devices are most likely conservative (referring to their psychological mental state and parenting methods, not their politics). We know a few things about these kind of people. 1 They value purity, cleanliness. 2 They value and respect authority (and laws) and therefore their authority as parents. 3 They value the "in-group" or "fitting in".
It seems to me this is what these parents intend to accomplish with a device: Maintain their child's purity, make them refrain from performing an impure action(s). I believe parents have their best intention when doing this.
The parent may be highly conscientious and low in openness to experience.
Low openness to experience. If they are low in openness to experience they will be less aware of their emotions and the emotions of their child, so less understanding of the emotional effect the device will have on said child. They will also prefer riged thinking over flexible thinking, so less seeing their child's point of view and more holding their view in high regard. https://en.wikipedia.org/wiki/Rigidity_(psychology) If a person with cognitive rigidity does not fulfill their rigidly held expectations, the following could occur:
Agitation, aggression, self-injurious behavior, depression, anxiety, and suicidality. These are in the case of someone who is extremely rigid in their thinking. Rather, I can see a parent displaying agitation and aggression towards their child only.
High conscientiousness. One facet of conscientiousness in particular, namely, deliberateness is quite apparent. The idea of your child getting into a "contract" with you as a parent. A contract to wear a device. It's natural for a person high in this facet of personality to gravitate toward plans and contracts. However, getting your child to make a contract or plan that they can't turn back on is absurd because children can't enter contracts at least not in the USA. (In the US, you are not legally a person until you reach the age of majority, eight-teen years old and therefore cannot sue or be sued, or enter contracts)
There is a reason for this, young minds aren't developed for these actions yet.
I can't give solid advice on how to resist coercion because every situation is different. There are nuances. One thing I can say is you can tell your friends, extended family, or authorities fairly easily unless they restrict your movement and confine you to your bedroom or something (which is illegal nearly everywhere). Just show your belt. They most likely won't want the eyes of the law on them or the possibility of their social circle finding out. It may be perceived as socially abnormal (a subsequent perceived ousting from the in-group at least in the parents minds) which is not something the parent will welcome and for good reason.
Children have the right to privacy. Chastity checks may be a violation of this (consensual checks are fine most likely).
No child should be punished in a way that humiliates or hurts them. Maintaining your child's purity, while noble in the parents view, can be perceived as degrading to a "liberal minded" child which may be a violation.
Nobody can do anything to your body that you do not want them to do, and grown-ups should protect you. This means parents should feed, clothe, give shelter, educate (homeschool or have them go to school), assist with hygiene (showers brushing teeth, ect), assist their child in transporting them where they need to be (for example an appointment to the doctor or dentist) to name a few. Wearing a device may be a violation.
Finally, I should address the elephant in the room, so to speak. Being chaste is a beautiful thing, worthy of admiration.
I have lots of respect for the ones who choose this lifestyle. It's not for everyone and that's the big takeaway. Some people are "liberal". They put less effort into remaining pure, opting instead to perform actions that chastity devices prevent. This is socially acceptable nowadays, and the parent should come to terms with it and move on. People will desire their own path perhaps different or the same as their parents.