Since Mike is a sociopathic arsebucket who is genetically incapable of understanding that the feelings of other people should influence his behavior in the slightest and who regards being asked to do so as a hateful burden by evil tormentors, this was an unnecessary and ridiculous obstacle to his need to have a maid and bedmate in his life right that second. Rather than risk her figuring out what kind of monster she was marrying, he had to find some way to shut her up. It was thus that he hit on the plan of having a private wedding ceremony so that Deanna could tell herself that she wasn't actually living in sin. Since she's not really all that bright and she doesn't like confrontation much, it would probably never have occurred to her to ask if the "minister" was legally allowed to marry anyone.
This means that whoever it was that suggested that the first wedding was the one for show meant to placate a gullible woman and protect Mike's right to let himself be made a stooge for Elly and John's plan to own his horses could well be on to something. It would also make Evil Mira into another evil person whose evil evilness comes from her evil habit of evilly and accurately assessing the situation and even more evilly saying what she evilly thought.