How do I get my daughter to understand that NO MEANS NO?

I'd say that you are being consistent and doing things right.

There is just one technique that I would suggest and that is to say, to her question about dessert "Yes, we're having fruit tonight, would you like an apple?" Try not to say No very often, if you can. It is hard for kids to rebel when you've said "Yes"

When you start doing this, you'll find that by saying "Yes" you eliminate a lot of your problems ..... when she asks "Can I play outside", instead of saying "No, because you left all your toys out", you now say "Yes, you can, as soon as your toys are tidy".

I also found by saying "Let me think about it" gave me some time to decide whether the answer should be yes or no, because in our house once I have said no, I don't change my mind. So my technique was this, I'd say "Let me think about that" and I told them not to ask again because right now its a maybe, but if they ask again it will change to a definite "No". Doing this gave me breathing space to come up with a correct answer for my children.

This will continue throughout your daughter's childhood and teens, so I found that saying "Yes" with conditions worked well - "Yes, you can use the car, but it needs to be washed before you use it", or "Yes, you can see your friends, but you can have them here for Pizza and a movie", or "Yes, you can go out, once all your chores are done", and "Yes, I'll give you a ride to your friend's place, but the dishwasher needs unloading while I take a shower" - can you see how to use Yes, rather than No all the time?

I teach preschool, and I hold my ground. If I say no, I mean no. If they keep it up. I will sometimes just hold my hand up and say "I said NO. But, you may do X". No you can't have dessert tonight, but you can help me make dinner tomorrow, or No you can't have that new toy, but lets go home and see what's in the toybox.

If my kids argue with me, I say "It's yes Miss Meg, and you do as I ask" and repeat it until they say it. I can't argue with 12-15 preschoolers...that's all I would do all day! There should be no back talk/arguing when you give an answer.

I'm sure things are new and different and it will take some time. Probably being with grandparents who may spoil her a bit is hard.

My dad was gone a lot with his job, once for an entire year, but that is no excuse...especially today with skype, email, cellphones, etc.

Ignore her if she asks for dessert after you've said no. Completely. If she carries on nagging, take her by the hand, remove her from the room, go back in and shut the door. She's not a baby - she is old enough to be at school for goodness sake!

She wants attention. If nagging gets her _less_ attention, she'll stop.

aww good mommy!

you can do it like Cesar Milan, the TSCH! method. Never yell or raise your voice at the kid. Use Calm ASSERTIVE energy with body language TSCH! After all the scariest people & the people with the most respect are the people who almost never yell.

When a dog gets out of hand cesar makes them submit. I guess in your case you have to give her a time out. & you need to work on maintaining her energy by making sure she doesnt get too excited like yelling at her your excited energy will make her excited & out of control. Work on being intimidating.

Make up a lie about dessert like say that dessert has been poisoned

After the 2nd time, she goes to her room.