I disagree with my Christian spouse's position on suing someone.
How do I handle that?

Your situation as originally stated in your submitted question is potentially the compounding of several questions:

1    What limitations are there on Christians suing someone?
2    Which spouse(s) may file a suit?
3    What if there is disagreement over whether to sue?

    The first point needs to be taken up with your church elders or pastor as it is primarily a doctrinally based question.  My reading of the Bible, particularly the New Testament, suggests that Christians are not to sue fellow believers, but rather attempt to resolve the situation through the church.  If there is no resolution, then the offended party absorbs the loss, unless the injury is criminally based.  If the injury is the result of the offending party committing a crime, then you might have a horse of another color, so to speak.

    Many years ago, my wife and I operated a retail business.  Many of our customers were fellow believers in several different churches.  One of those customers took delivery of a gift for their daughter, but did not pay the bill when due.  After contacting them directly, they stated emphatically that they had no money to pay the bill, now or in the future, and were not going to return the merchandise because they were determined to give it to their daughter on her upcoming birthday.  Faced with economic loss, we contemplated a lawsuit against the couple, but a check in the Scriptures affirmed that that move was unacceptable.  As we saw things, we had two options that were pleasing to God, take the loss on the chin, or attempt to resolve it through that couple's church as a disputed sin issue.  We first contacted their pastor, presented our side of things, and gained his "witness" that what that couple was doing was nothing short of stealing.  He then approached the couple, but no repentance was in sight.  He gained further support from other church members ("witnesses") as to the sinful nature of that couple's action, and after a period of time they provided us with payment for the goods.  I was quite pleased to see their church carry out its God ordained mission in this area.

    As to which spouse may file a lawsuit, it is again a doctrinally based issue that might also be complicated by your local laws.  It appears to me from my reading that either spouse may file a lawsuit, but if the wife is the plaintiff, she is to do so only under her husband's direction.

    As to couple discord regarding the filing of a lawsuit, the focus of concern is the discord, not the circumstances which prompted the discord.  If the wife is filing against her husband's direction, then the discord is the result of rebellion against God's ordained order for the marriage relationship.  It has been my experience that persons who rebel against earthly authority are also likely to be in rebellion to God, and this can be seen in their relationship to Him and their fellow man.

    If the husband is suing against the "better judgment" of the wife, then we have a difference of opinion or preference, not an issue of sin on the part of either spouse.  The wife is to go along with the husband's direction and even be supportive in her actions.  I see no admonition in Scripture, however, that the wife is to change her mind on the subject -- she can stay with her conviction that suing is the wrong move, but she is not to harangue or harass her husband after she has stated her preference or opinion.  She is to carry out his requests for assistance as though doing it "unto the Lord."  If she does not do so, then it is likely that this same behavior is evident in her relationship to Christ, that is, she only obeys Christ when she "agrees" with Him.

    If the wife's judgment call is indeed the sounder of the two, and the husband does not heed her counsel, then the husband likely has a pattern of either not recognizing wisdom when it is placed in front of him, being in rebellion to wisdom, and/or holding a debased view of his wife and/or women in general.  Any one of these will result in unnecessary grief to himself, his family, and those around him who are impacted by his behavior.  By the wife going along with his unwise choice, and doing so with the same degree of support she would give to the Lord, she accomplishes two things.  She "allows" her husband to experience the full negative psychological impact of his behavior, and also maintains oneness with her husband.  When the "fecal matter interfaces with the air circulating device" (let the reader read that in whatever language he/she sees fit) the husband will feel the pain he has brought not only on himself, but on his loving, committed, faithful, and supportive wife.  This is usually too great a load to bear, and the man's pride and/or stubbornness is broken.

    For such men, this is often the only medicine that works.  He is crushed by his own anger which he cannot pour out upon his wife because he knows that she resolutely stood by his side through the whole mess up.  However, had she abandoned his side for whatever reason, he would quite likely blame her for the failure, pour out his wrath on her, deny in whole or in part his accountability, and go on about his life an unchanged man ready to repeat his error.  And for the wife who endures the hardship brought on by her husband's folly, she shows the love of Christ in that she was willing to suffer as an innocent party in order that her husband might be set free to be a more Godly man.