(Makes one wonder which spouse is wearing the pants in this family.)
By “legal” you must mean "is the wife a proper party plaintiff or claimant?".
Whether she is a proper party to the lawsuit would depend on whether she has some recognizable interest in the subject matter of the litigation that would be affected by the outcome. And if so, it could make her not just a proper party but a necessary party to the action.
Of course, not knowing the nature of the claim or the marital property laws involved, that is mere speculation. But what practical difference does it make if she is in or out, joined or not joined in the law?
This verbal agreement you mention undoubtedly results in but one cause of action or claim against you, one scenario of evidence, and one judgment - good or bad.
Why don’t you concentrate on the merits of the claim against you, rather than who is entitled to pursue it?