L.N.
I don't have any real advice, what you're doing seems to be what we're doing. But I just wanted to say that I have a group of friends and we all have 3 year old girls. There are 9 of us and we are ALL experiencing what you are with your daughter. We all agree that whoever said "terrible 2's" was mistaken, it's the 3's. We all deal with it in our own ways. You just have to find what works, though I find that we have to change it up a bit every now and then. It sure is tiring though, especially with an infant at home too. (My son just turned 4 months.) I have heard lots of good things about that "Love and Logic" book that was mentioned. I also really like "The Happiest Toddler on the Block".
You're not alone, it's just tough!