Can a parenting coordinator change a parenting schedule without both parents' consent?

This depends entirely on what authority the parents gave the coordinator in their parenting coordination agreement. Many agreements do give the coordinator the ability to make binding decisions about the practical details of an existing schedule, such as adjusting exchange times or resolving disagreements about how a specific provision applies, without needing both parents to separately agree to that particular outcome; that's the whole point of giving the coordinator decision-making authority for these kinds of disputes rather than requiring fresh consent every time.

What a coordinator typically cannot do, even with broad authority over day-to-day disputes, is fundamentally rewrite the parenting arrangement itself, such as changing which parent has the child on a long-term basis or significantly restructuring the overall schedule, since that kind of change usually falls outside the scope the parents agreed to give the role. Where a coordinator does have authority to adjust specific schedule details, their decision is generally binding on both parents even though one of them disagreed with it, which is different from needing fresh consent. Reviewing the agreement's specific wording with a family lawyer clarifies exactly where that line falls in your situation.