Do we incur sin if we leave the house of the husband's family, despite his mother's refusal, knowing that the cause of the problem is the husband's sister accusing us of theft without proof?

It is the wife's right upon her husband to provide her with an independent dwelling where she will not be harmed. She is not obligated to live with his family, as that might cause her harm. The husband is not obligated to obey his mother in not leaving her house, and he does not sin by disobeying her in that, but he must continue to honor her and treat her kindly.