OK, it's been awhile since I've read UP: But my sense is that the bottom line was: Discipline by punishment is ineffective. Kids need unconditional love. I take everything else with a grain of salt.
What I didn't like about UP was that it was dreadfully short on strategies and specific kinds of things that you can do.
In your situation, I would have looked at my child and said "I need to go in. I'm tired, cranky and hungry. I need breakfast." Period. 90% of the time, that would do the trick. If not, I would have commiserated with my child as to how hard it is to leave when you wanted to say. I would have, if needed, resorted to picking my child up and moving her out the door.
Is that UP? Probably not. But it beats the alternative - my lashing out at my child verbally and/or physically. I've learned dealing with dd, that when I hit the edge I need to leave NOW. I see red and do things I'm ashamed of. I'm working really hard on that. One strategy is to recognize my limits BEFORE I hit them, and simply draw the line. "It's time to go." Period. No discussion. I'm done. Loving my child unconditionally means that I need to be able to control myself enough not to harm them. But it also means that I need to be able to take care of myself enough so that I have the reserves to behave like an adult should.
Chores: We've struggled with this, but the situation that works the best for us is doing them right after dinner, before the kids go out to play. When the chores are done, they get to go out. Is that coercive? Probably. Does it prevent whining (on the kids' part) and yelling (on our part). Yep. In this situation the positives (learning to do real work around the house, contributing to the family in a meaningful way, learning to do things that need to be done to make a family work even when you don't feel like) outweigh the negatives (indirect coercion).
Note that this 15 minutes of chore time was something that dh and I did before the kids were born. We instituted it because we too had a hard time doing the things that needed to be done, but we didn't like to do (such as cleaning the bathroom).
Bedtime: We have a routine that's pretty inviolable. Pajamas, snacks, reading, toothbrushing, stories in bed, lights out. It's just what's expected. It's not coercive. It's just what we do. Even when we've had a terrible day, we get snacks and stories.
