So let's say you're the attorney for the spouse. We've been referring to this person as "him" so your client is the wife. She says " . . . and I came to you in your office in Houma because my husband went and visited every known divorce lawyer in New Orleans so that I couldn't hire any of them."
You then have the husband in deposition. If you're any good, you ask him about this process that he went through. Unless he's very very bright and slippery, it will be pretty evident that he was only trying to conflict out the divorce bar in NOLA.
And really, this isn't something that you - the spouse's attorney - are really looking to "prove." It's more of a character thing that you want to get on the record and find an appropriate way to bring it to the judge's attention. Perhaps you can incorporate it somehow into a motion. Or at trial, you might be able to bring that testimony out. It's a strategic thing rather than a point of contention in the litigation.