Did the husband wrong his wife by divorcing her due to her lack of commitment, and what are her rights after divorce according to Sharia?

The questioner's wife is in error and rebellious, and divorcing her was not an injustice. Rather, divorcing a woman of bad character is recommended, even though the preferable approach would have been to follow the Sharia-compliant steps of admonishing her for her insubordination through its stages before resorting to divorce.

As for the financial rights of the divorced woman: A disobedient wife (nashizah) who is revocably divorced has no right to maintenance or housing until she ceases her insubordination. If a disobedient pregnant woman is divorced, she is not entitled to maintenance.

As for the non-material rights: The mother has the right to custody after divorce as long as she does not remarry, unless she neglects her duties of custody or her immoral conduct is proven. In such cases, custody transfers to the next eligible person, as determined by the Sharia judge. Mere insubordination does not forfeit the right to custody.