Will the one who gives charity from his family's money – whether it be for personal expenses or a remaining portion of household expenses – be rewarded, or does the reward go back to the family, and is this charity considered showing off?

What is given in charity from personal spending is permissible if the money is owned [by the giver], and a person has the right to dispose of their property as they wish within the bounds of Islamic law. If the family authorizes the disposal of surplus money allocated for purchases, it is permissible to sell it, give it in charity, or gift it, and the doer will be rewarded if they intend it for the sake of Allah. However, if they do not authorize it, it is not permissible to dispose of the money, and it must be returned; whoever disposes of it is accountable for it. Waswas (whispers of the devil/obsessive doubts) when giving charity is a demonic deception, and a Muslim should seek refuge from it, do good deeds, and strive to achieve sincerity. There is no specific supplication to be recited when giving charity, but one can supplicate that Allah accepts the charity and makes it purely for His sake.