There are general, vague communications clauses in almost every custody order, so yes - you can file for contempt of court and yes, a judge can find her in contempt. Best you can do is continue to try to make contact. Continue to document failures for callbacks or videoconferences. Have at least one of your team be there as witness as they are able, you could use their sworn affidavits later or maybe they would even appear in court on your behalf to testify.
While it's unlikely that it will result in a custody change, these are the situations you use as the impetus to request changes to, not only the communications issues, but to the custody order itself in terms of the parenting time. Just because you won't win it doesn't mean you don't ask for it.