From what I know about assisted suicide or euthanasia it is not a decision which is taken lightly by the doctors or hospitals. Just because you come to this decision either for yourself or someone else you have legal guardianship over (part of the research I did was about euthanasia for older people with dementia in European countries) it does not mean you get the medications right away. There is a process involving interviews, psychiatric evaluations with the person and their guardian(s), consultations with physicians outside of the case, and so on. At any time the patient/guardian is able to change their minds. The doctors, including those who evaluate the patient that have otherwise not been part of the case, can recommend against it. The patients, if lucid enough, have to put their wishes in writing several times. I would assume that the same thing would happen with terminally ill children who ask to be allowed to die or whose parents come to this conclusion. It is not as simple as saying "Give us the medication so my child will not wake up" as Hollywood might portray euthanasia cases.
I'll admit, I am a supporter of the right to die with dignty. As a parent, this would be the hardest choice I would ever have to make regarding my children. I can't say what I would do if faced with that.