There isn't enough information here and an academic answer in the abstract isn't warranted. I'd want to see both halves of the text message and any associated declaration, record of testimony (or at least a detailed recollection of the testimony), any written argument given to the Court to rule on the admissibility of the text message, the Court's minutes, any Court order for any hearing on the matter, and any verifiable position of the other parent or his/her attorney.

What I have learned in family law, as I have been practicing in it for a very long time, is credibility matters to some judges, and to others, it means nothing. I have flat out, cross-examined witnesses who have lied right the judge's face, and it did not matter, it is shocking frankly. But, I do know one thing. I am typically on the side that does not lie, is very credible in Court, does not cherry pick evidence, does not try to mislead the Court, and we are usually a little more successful than the opposing party, if not prevailing 100%. I would bring it to the Court's attention, either in an opposition or during examination. But it really depends on what the issue is.

You need to learn how to bring it to the courts attention, either by "impeaching" is oral or documentary evidence or by independently authenticating the full message and testifying and/or introducing the evidence yourself. If you don't bring it to the court's attention in a timely manner, you lose your rights.