Yes, I would. Two reasons why. First, as a judge, it would be my job to enforce the entire law, not just laws that I like. It's easy for you and me to say to go light on Luther. We don't like the law she's violating. However, as a judge, that isn't supposed to matter.
Second, bear in mind that she wasn't being jailed for the underlying offense of opening her salon. She had already received a verbal instruction on that. She was being jailed for contempt of court. That's a separate offense. When a judge imposes a punishment for contempt, it's supposed to be severe enough to deter continued contempt and to encourage others not to do what she did. Well, she basically told him to screw himself and that she was reopening her salon whether he liked it or not. In light of that, I'm not sure what other measure he could have taken that would have ensured compliance or what level of contempt she'd have to show that would justify incarceration.
Let me throw this out there. This doesn't have to be binary. It's possible for both of them to be right. I understand why she wants to reopen her salon, and frankly, I sympathize with small business owners. They're getting massively screwed in this, and the political media and most Democrats are largely unsympathetic to their plight. In fact, their plight is often approached with scorn and ridicule. However, I also understand the plight of a judge whose job it is to ensure compliance with the law whether I agree with the law in question or not and whether I like the politics of the judge or not.