Skip the contempt charges!! It will cost you way too much and this can be handled better by YOU writing a strongly worded letter requesting the phone number. Or better yet, have your attorney write and send the letter.
By the way, are the children in daycare/school? If so, you have right to the information contained in their emergency contact file. There you will find the unlisted phone number.
If she didn't update it at school, have your attorney include that information and point out how that endangers the kids by the school not having a valid phone number.