Once it is refrigerated, it takes a very long time for it to separate again.
Like, forever.
And no, you can keep it in the fridge right-side up.
Well, I did say a very long time. 
To be honest, I can only *assume *it separates again at some point.
I have a special peanut butter bowl. I dump out my natural peanut butter, stir it up until it’s all mixed, then refrigerate. It solidifies something fierce, but 15 seconds in the microwave takes care of that. Then back into the frige.
After the first time I stir it, I only have to give it a brief stir occasionally. But I have peanut butter toast for breakfast every morning, so a jar only lasts a couple weeks.