Boy can I relate to you!! My husband and I have similar run-ins regarding our 3 1/2 year old son.
By the way our kids have gone to the same bedtime training camp apparently, our bedtime routine is similar and its also a time when my son loves to test every rule and boundary. I always figure he's just getting a few more hoorahs in before he has to spend 10 hours not saying no or whining about anything :)
In our house, what helps is that my job actually involves kids, development, and behavior management so despite our heat-of-the-moment issues, in general my husband defers to me. BUT, what I find is that I have to talk to him about when we're not both frustrated with our son and each other. So for you I'm wondering if, at a time when you are both calm and happy, you could say honey, I think we need to get on the same page a little more for DD's discipline so that it works better for her. You are absolutely right that following through on threats is really important. What I always tell my husband is that, as hard as it is, discipline has to come down to cause and effect, not emotion. So even though you're boiling mad at your DD for whining or saying no or throwing a fit, the only message she needs to get is when I do this, that happens. Period. So when your husband comes and undermines you, it messes with that. So maybe you could put it in the context of what is good for her and that may help him see it?
I know partly you're just pissed at him, and I would be too!! This is a generalization, but in my house and in most other families I know well, the mom does like 90% of the disciplining because the mom does like 90% of the actual care-taking and those are the moments when kids don't want to cooperate. So when Dad decides to take his head out of his...TV show...to drop his two cents into the mix, its infuriating.
I know for me, some of my anger in those moments goes beyond the situation at hand. Its frustrating when you do most of the work and instead of appreciating everything you do to make the family's world go round, he tells you you're actually not doing enough!
Having him be in charge of the bedtime routine for a week or so could help, but I would say you should lay some ground rules so that your DD has consistency and so that your husband has to do the work of holding her to the same standard as you do. If she's supposed to be putting on her PJs and brushing her teeth by herself, he can't just start helping her and then say, see, she's easy! And for her sake, she can't become a pawn in the game of which parent produces fewer fits (I know YOU'RE not looking at it that way, but I think Daddies do sometimes!).
Good luck and hang in there! Your DD is lucky to have such a committed, firm parent who is willing to do the hard work!!!