Is it obligatory to change a false testimony in court, despite the parents' refusal, and what is the effect of that on the relationship with them?

It is not permissible to wrong the husband to please the parents or to obey them in disobedience to Allah. Therefore, you must strive for reconciliation with your husband. If he insists on not returning, then either change what you mentioned and speak the truth if no harm will befall you, or withdraw the case and drop it. There is no sin upon you if your parents become angry, and you should strive to appease them through supplication and the mediation of righteous people.