I am finding it hard to submit to my husband when I disagree with some of his choices around how our lives run. How am I meant to obey 1 Peter 3 when I feel my husband's actions violate God's word?
A woman's obligation to submit to her husband's authority should never be dismissed lightly, and is similar to every Christian's obligation to submit to church leaders or government. So far as it depends upon you, be at peace with all men and women, striving to obey the authorities placed over you in a sincere desire to please Christ.
These authorities over us will not be perfect, of course, since all human beings are sinful, and yet Christ asks us to obey them knowing full well they will sin at times. The Bible doesn't say, "Obey authorities except when they sin," or "obey authorities except when they ask things you don't like or don't agree with, etc.". So the same goes in a marriage.
The only time we can knowingly disobey an authority over us is when that authority requires us to do something that is directly contradictory to the commands of Scripture. Even then, we should do all we can to obey, at least in part, while narrowly avoiding sin. The heart of submission will always look for a way to obey, while the heart of rebellion looks for any excuse not to obey. Remember, Abraham asked Sarah to go along with his lies to Pharaoh, and although she did not participate in the lies herself, she did concede to his requests and obey him by following his (bad) plan. This is the example of submission held out in Scripture by Peter:
There are many instances in life when a wife may struggle to submit to their husband. For example, filing a law suit again a neighbor. Paul instructs the church in 1 Corinthians 6 not to file a suit against a fellow believer (neighbor), so if your husband is doing so, you should advise him on Scripture and try to persuade him to do otherwise. In the end, if he chooses to move ahead with the suit, then you should support him nonetheless and cooperate with him without sinning yourself (like Sarah). On the other hand, there is no command in Scripture against filing suits in court against unbelievers. So if your husband files suit against an unbelieving neighbor, then you have no reason to object to your husband's wishes.
What if your husband asks you to do something that offends your conscience, such as watching R-rated movies? If the movie presents images of one kind or another that you find to be sinful, you have liberty to avert your eyes or leave the room altogether. When your husband is asking you to go against your conscience, which is sin, you may act to preserve your conscience over your obligation to submit to him. Having said that, we strongly advise caution in using the reason of "conscience" to engage in disputes with your husband or to challenge his authority. It's easy to label personal preference or desires as a matter of "conscience" whenever it suits our desire to avoid submission, which is a game of disobedience that God sees through. We would also recommend reading "Why is watching pornography sinful?" and initiating a conversation around what types of images or movies you may both feel comfortable viewing.
If your husband chooses to walk away from Christianity to follow a false religion, then this is clearly a path of disobedience on which you cannot join him. If your husband was not a believer in the first place, then your obedience to your husband cannot overrule your obedience to Scripture. Continue to honor your husband in every other possible way, but do not allow his move toward idolatry/false religions to compromise your walk of faith. In speaking about the importance of believers not entering into religious unions with unbelievers, Paul says:
We would also encourage you to read "Can a believer marry or date a non-believer?"
The battle over submission in a marriage can be heated. If it appears that the husband is not leading his family in keeping with the biblical model of spiritual leadership, and the wife appears to be in conflict with him in multiple areas of marriage, this is not a healthy state of life for a Christian couple and we would recommend they seek biblical counseling with a local church. But remember above all, the first duty for both a wife and a husband is to Christ first. When we obey and honor Him, the other areas of our life should likewise follow His example.