If you file for contempt, then there is a strong possibility that she will file for contempt. You may be able get proof during discovery but you need to decide if it is worth the risk of your ex filing a contempt against you.
Sounds like you should have a specific consultation with an attorney about this.
If you are skeptical of the evidence, then objectively there are likely problems. But these things may be overcome with some suggestions and advice.
I agree with my colleagues that by filing a Complaint for Contempt you are opening yourself up to your ex filing a Complaint for Contempt against you. However, I would suggest having a consultation with an attorney to discuss the facts of your case, and the circumstances under which each of you are in Contempt.