Would my mother be considered disobedient to her mother after she denied my grandmother's claim that her belongings were stolen, which caused problems for her grandmother?

There is no obedience to a creature in disobedience to the Creator. Injustice, falsehood, and calumny are blameworthy characteristics, and accusing an innocent person of theft is a great and forbidden injustice. What the mother did by acknowledging that no theft occurred is a testimony of truth that was obligatory upon her, and it is not permissible to conceal it, whether the person testified for or against is a relative or a stranger. As for the grandmother's insistence on a false accusation, it is an evil that Allah has forbidden, and it is not permissible to condone it; rather, she must be prevented from it and warned of the seriousness of the situation, for those who harm believers without cause have committed a manifest sin. The mother must explain the legal ruling to her mother and clarify that she has defied her wishes to please Allah, urge her to repent, and strive to appease the wronged person. The mother should continue to maintain ties with and be dutiful to her mother, even if the grandmother cuts her off, for pleasing Allah is above pleasing a creature.