Other than examining yourself on the points your wife relates back, making amends where amends are due and changes where changes are due, there is not much more you can do. If you’ve done what you can to make it as easy as possible for someone you’ve wronged to be honest or forgiving, it is up to them to do the rest.
Unless she starts telling lies about you that anyone who counts is actually going to believe, I would leave the door open and move on.
Your wife, however, might get a little spine and tell your relative to quit wasting her time and either talk to you directly or get over it. “Aunt May, if he does something to you and won’t do a thing to make things right, you’re welcome to talk my ear off. But every time he asks you, you say it is all fine. If it’s not all fine, then admit it instead of fibbing about it. If it is all fine, then drop it… or at least quit running down my husband when I’m around. It’s getting old.”
On the other hand, maybe as far as your wife is concerned, Aunt May isn’t getting old. Your wife may not admit it, but the two may be doing nursing time on each other’s grudges against you or throwing little pity parties for their mutual grudges against the family as a whole. In that case, Aunt May is the least of your problems.