Is it permissible to use zakat to pay the reconnection bill for electricity and water meters for a poor family (the wife's family) who were unable to pay their bills, which led to the service being cut off?

If the aforementioned family is poor, there is no objection to paying Zakat to them. You must give it to them and empower them with it, and they may do with it as they wish. Do not pay their bills for them unless they ask you to pay an electricity bill or other bills when you give it to them.