Handling a toxic situation in a family business (no HR, need advice)

TL;DR: colleague in family business has been speaking negatively about me publicly; I have evidence and it affects work. HR isn’t an option. I still need to work with them daily and want to handle it professionally. Looking for advice on boundaries and next steps.

Honestly, I’m in a really tough spot and could use some outside perspective.

​I work in a family-run business, and lately, a colleague has been discrediting me publicly. It started with a few snide remarks here and there, but it’s escalated to the point where it’s actually messing with our day-to-day workflow. I’ve even got screenshots of the messages and public comments they’ve made, so I know I’m not just overthinking it.

​I’ve tried to handle this the "right" way—staying professional, trying to settle things internally—but nothing has changed. The situation is just... stuck. Since it’s a family business, there’s no HR department to go to, and the dynamics are already pretty loaded. I still have to see this person every single day, and I really want to keep things mature without causing a huge scene or making family dinners awkward.

​At the end of the day, I just want some basic respect at work. I don't need us to be best friends, but the constant undermining is exhausting and making it hard to get anything done.

​Has anyone else dealt with something like this? Especially the "no HR" or family business aspect? How do you set firm boundaries without making the drama worse? Any advice on how to handle the next steps professionally would be appreciated.

​Feel free to DM me if you want more of the backstory or specific details. Thanks in advance.