No, the mother needs to communicate her concerns to the father and insist on improvement, but not refuse visitation or use the child as a weapon or even involve the child in any conflict. Kids are loved, are not to blame, are not spies, and are not weapons of marital war, otherwise they might be moved to where that doesn't occur . For failure to pay support, however, see an attorney our see DHS and ask for child sport enforcement assistance, which will get the State Attorney to take action. That is protecting the child. Take the great course at www.proudtoparent.org and encourage your ex to do the same. The kids are the future, remember them and what they want and need is top priority.
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk. I am licensed in IL, MO, TX and am a Reg. Pat. Atty. so advice in any other jurisdiction is general advice and should be confirmed with an attorney licensed in that jurisdiction.