Is a man's prayer with his wife in congregation considered sufficient in lieu of prayer in the mosque, and is it better to pray with her at home when there is no nearby mosque, or to pray in another congregation?

Congregational prayer is obligatory for adult men, and it is best performed in the mosque. If you pray at home with your wife in congregation, that is permissible, and the obligation is fulfilled. It is better to pray with a group of people because their number is greater, based on the Prophet's (peace be upon him) saying: "Indeed, a man's prayer with another man is purer than his prayer alone, and his prayer with two men is purer than his prayer with one man, and the more numerous it is, the more beloved it is to Allah." Some jurists hold that there is no superiority of one congregation over another, based on the generality of the hadith: "Prayer in congregation is twenty-seven degrees better than prayer performed alone." According to this latter view, your prayer at home would be preferable in order to attain the reward of congregational prayer for your wife.