Is a wife entitled to abandon her husband in bed and deny him all his conjugal rights, claiming he does not spend on her, even though she knows she lacks nothing and they live a better life, and is this considered an ungratefulness toward her companion?

The husband's spending on his wife is obligatory, and your father is still providing for her, because the children's expenses on their mother are considered spending from the father. If your mother receives sufficient provision from your and your brother's spending, then she has no right to further provision from your father. Therefore, your mother's refusal of your father, under the pretext of lack of spending, is not permissible, and she is considered disobedient (nashiz) and sinful.

The mother must be advised, for denying the husband's kindness is a form of ingratitude towards the spouse, for which the Prophet, peace and blessings be upon him, threatened with Hellfire those who do it.