If one partner has that degree of mistrust and doubt about the other, there is no relationship. That’s just two people hanging out pretending to be in a relationship.
If one partner can’t tell the other they are suspicious or concerned about something, ask about it, and talk openly about anything under the sun, there is no relationship.
If one partner has such little self control, and such a bizarre sense of right & wrong, and ultimately acts out in jealousy/anger/confusion/whatever, that person is emotionally a child, and there is no relationship.
Unless it swings both ways: if neither one trusts the other, if neither has a conscience, if such moments of “weakness” are typical of both people, then it’s likely a match made in heaven. They deserve each other, mistrust, second-guessing, secrets, and all.
I agree with @hug_of_war – a moment of weakness is indulging in ice cream, this is WAY beyond that. And I agree with @Jeruba – I would be outraged. I’ve never heard of anyone doing anything like this, and can’t imagine anyone I know encountering such a thing.