Is it permissible to make a vow in cases of recovery, and is it permissible for my wife to fulfill her vow from the household savings with my consent?

The wife's conditional vow, though disliked by scholars, must be fulfilled if the condition upon which it is suspended comes to pass. The wife is obligated to fulfill her vow in the manner she intended. As long as the cost of the sacrifice comes from the husband's money and with his consent, she should slaughter it and distribute it to the poor and needy. Vows are disliked in general due to the established prohibition against them.