His Purpose: Sanctification
According to Ephesians, Christ's purpose and duty to the Church is to sanctify and cleanse. Understanding this as the core purpose will help enhance how you pray for your spouse. It will also help you withstand any attack of the accuser, because you know why you're doing it. There's no shame in men speaking to God on behalf of their wife and family. As you pray for and with your wife, the effects will trickle down to impact the entire spiritual condition of your home.