Generally, if the parents speak clear English, someone will pull them aside, explain what is going on, and if they want to stop, their wishes will be honored. Of course, the kids I saw die in the PICU were those with life-threatening diseases: pulmonary HTN so bad that the child had to be heavily sedated to not go into crisis, children with really complex cardiac anatomy, children that are probably brain dead but haven't been determined to be so yet, etc, so most of the time, the entire team agrees with the course of action. In the particular case above, we were getting ready to send the kid to the floor, so we didn't think the kid was on that downslope of disease, but some of the nurses still had a lot of problems with the decision.
This is why those type of discussions are crucial in the PICU (and other ICU settings), because it's really hard to get a clear idea of wishes when a patient is circling the drain. We have a surgeon who refuses to talk to parents about DNR/DNI while their children are in the PICU following surgery, even if the child isn't doing so well, so there is some tension in that mentality as well.
In emergency situations, consent is generally not required for life-saving treatment. In certain situations, a court order can be obtained to overrule the parents (as in cases of Jehovah's Witnesses and blood transfusions, especially in minors), but these generally aren't decisions that are made in emergency situations; they're done when the risks and benefits of treatment are considered and the parents choose to forgo what is deemed to be life-saving treatment (chemo, blood transfusions, etc).
So generally, in absence of a sit-down discussion with parents, the default is full code and full resuscitation, parents' wishes be damned.