Shes running off whenever we are not at home

Wait, what? Are you leaving your 4yr old home alone?

But no, you don't cancel Christmas, especially not for a 4yr old. Taking away the biggest holiday of the year for a kid isn't going to send the right message. It's overly harsh and is just going to lead to resentment.

Hell, my nephew's being released from a juvenile detention facility 4 days before Christmas and I'm getting him a gift - that kid needs more love and support right now, not less.

Reasonably punishing a child makes sense for average kid stuff (taking away Christmas is not reasonable), but it's rarely what fixes serious behavior issues.