Again, H., sounds a lot like my little guy. I agree with Maura, it sounds like she's testing her limits and she knows she can get away with a lot right now.
My son does the same thing - we remind him to tighten up his listening ears (which works with a younger kid) and if that doesn't work, we move swiftly to take him out of the situation he's in and enforce consequences for not listening/following directions. It sounds harsh, but 2 minutes in the "thinking chair" (we don't call it time out) for him to think about how he needs to behave usually does the trick.
The biggest challenge for us has been being consistent with enforcing whatever consequences we lay out. It's easy to keep saying, "tighten up your listening ears" but eventually it loses meaning when you don't have anything to back it up. So, we try to remind him either once or twice and say, "next time, thinking chair." Then we have to stick to next time thinking chair.
One thing I try to never do is respond to the tantrums. I try to ignore them as best I can (much easier when you're at home than out in public) then when they subside, we talk about good behavior and what we expect from a big boy. I try to never label him as good or bad, but talk about how a big boy behaves... sometimes that gets challenging too!
It's frustrating, and I know when we've spent a lot of 1:1 time together it's even worse because we get tired of each other. My best advice is to stay consistent, remember you're the mom and you set the rules and also remember that you are doing a great job. You are giving your daughter a gift by spending time with her and trying to be the best mom you can be.
It's good advice to take a time out for yourself when/if you need one. Know your limits - even if you can't escape totally for a few hours by getting a babysitter, it seems like your daughter is old enough to have 20 minutes of quiet time so you could take a shower, a bath or just sit in a room by yourself and decompress by reading a magazine or something. I know sometimes taking 5 minutes to myself in the bathroom with the door shut when I know my son is safe, occupied and in no danger is the best medicine and can help me get through the rest of the day!
One last thing - sometimes turning a frustrating situation into a funny one is the best thing for us. We still get our point across, but when you're not locked in a battle of wills (which can get heated at our house! We're all stubborn!) you can sometimes get a lot more accomplished.
Anyway, long response, but I hope it helps out!
Good luck!