Is it permissible for a woman to claim in court that her husband squandered the furnishings (furniture) to obtain her dowry, knowing that she agreed with him on a nominal dowry in the contract to reduce expenses?

The correct legal seclusion (al-khalwa (definition) al-shar'iyyah al-sahihah) carries the ruling of consummation (al-dukhul), and by it, the full stipulated dowry (mahr), both the promptly payable (mu'ajjal) and the deferred (mu'akhkhar), becomes due. You have the right to demand it. This includes the list of movable assets (qa'imat al-manqulat), which is considered part of the dowry. It is not permissible to resort to lying to obtain a right unless it is impossible to obtain it through truthfulness. The wife's right is firmly established as a debt upon the husband, and even if she cannot obtain it through judicial means, she will take it from his good deeds on the Day of Judgment.