I make a lot of vinegar based sauces. you can really play around with the ingredient, which is fun. When I’ve done it, i blend everything with the vinegar then simmer for 20-30 minutes. toss it in the blender and then you can strain it out. I found that if i strain it, it will seperate. Best solution i found to avoid it is to just add a little xanthan gum. It thickens the sauce a small bit and keeps it from separating.
Lately I have been playing around with fermenting. I use a 2.5% salt to fresh ingredients by weight ratio. toss the peppers and anything else into a vacuum sealer bag with extra space for the gases it will create, add your salt, seal it up, and wait for 2 weeks. then blend it.