No I didn't sand between coats, it didn't even occur to me that I should. I'll do a third coat then, and sand before I do. I just figured I was applying it incorrectly.
I'm going to give it a couple days to dry completely as you suggest. I have to work on the other pieces anyway. My goal is to have this done before next weekend is over. But now I'm starting to think about putting a top/hutch on it to hold a set of lights. Maybe that can wait for a few months.
It wasn't as hot here today but tomorrow it is supposed to get ugly again. I'm in Denver, CO so there isn't much humidity, basically desert. But the Sun is intense at a mile above sea level. Also I've moved everything inside, the house smells like a chemical factory but it is worth it to not have cotton sticking to the polyurethane and stain.
I just stained the decorative trim for the top edges. Hope I end up using it instead of wasting it like I did the 1/4 rounds.