It's not just a girl thing, my 2.5 year old guy was doing the same thing this morning. My approach is not to let him know it bothers me, to make him accountable for it, not to reward negative behavior, and to show him I love him in spite of the negative behavior.
He grabbed the remote a bit ago and turned Sesame Street off. OK, if he doesn't want to watch it I'm not going to make him. I took the remote and put it up high and he started crying he wanted to watch it. i said, "Then sit down and I will turn it on." (He'd already jumped down and was playing.) He said, "No," and I responded that the TV wouldn't be going back on until he was sitting...he was determined it would go on while he was running around. He proceeded to start whining and trying to get to the remote and I told him if he kept it up he was going to his room to sit in his bed, he REALLY didn't want that but kept crying and whining. I tried to calm him down and explained that he needed to sit if he wanted the TV on, and that I could not understand him when he whines, but he wanted to continue to whine. So I picked him up and we started to go to his room and he quieted down, said he wanted to watch Sesame Street. I asked him if he was ready to sit down, he looked surprised, I asked again and he said, "Yes." So I turned around and walked back, sat him of the sofa, turned it on and he's answering Cookie Monster about the "letter of the day" right now ; )
Things I've found that work are:
~ Keeping my voice calm and matter-of-fact. No yelling unless he's in a life-threatening situation, i.e., he was going to run in a parking lot or into a street. Part of continuing to whine is that toddlers or older children know it bothers you (I say this collectively of all parents) and assume (often rightfully) that you're more apt to give in to them, which I'm not.
~ Stating my request in the same words so as not to confuse him. I've found if I rephrase what I'm saying he thinks he seems to think he's winning the "argument", not sure why that is.
~ Going on about my business as if I don't hear him, he may get mad because I'm "ignoring" him, but he sometimes stops the whining because he's learning that I "can't hear or understand a whining or crying voice." As soon as he speaks in a regular voice I pay attention to him (rewarding his good behavior) and tend to his request.
~ Making him accountable for his behavior in that HE needs to stop doing what HE's doing, the crying or whining, because it's not acceptable. I will give him the choice to get what he wants or whine, but not the two at the same time. If he asked for apple juice and whines after getting it, I take the apple juice away until he stops. (No rewarding negative behavior.)
~ If he doesn't stop the whining I make it clear I don't have to and won't listen to whining and crying, and he's going to his room where he's free to whine and cry all he wants. The thing is, 4 out of 5 times he stops before we are in his room (I take him by the hand and if he refuses to walk I carry him.) If he is finished we go back to what we are doing, he can politely ask for what he wanted and we go on from there. If not I close the door and he may scream but I don't go back in until he's quiet, which is usually a minute or so, I realize he needs that time to himself to regroup and calm down. Whenever he calms down I thank him for stopping the crying and/or whining, ask him if he feels better (sometimes he tells me "no", lol) hug him and remind him that we don't whine or cry for no reason, and ask him if he understands. He always says "yes," but I know it's the consistent handling of the whining that will help him to really understand.
~ Recognize that if he's having a meltdown he may be tired and need a nap or to go to bed earlier. Most of the time when he starts whining and I ask him if he wants to take his nap (he still naps at least an hour each afternoon) or go to bed he jumps on it and says "Nap!" or "Bed!" and starts saying "goodbye" or "goodnight", hugging everyone and runs to find his bear, Arnold, and Puppa, his Pillow Pet so he can go to bed.
~ Show my love and understanding when he's upset, which doesn't mean I'm going to let him have his way. I let him know I love him and hug him (sometimes he pushes me away) and tell him I hope he feels better soon, but that he can't keep whining. Sometimes he nods his head like he understands or says "I know." ; )
The thing I've found that helps the most in dealing with toddlers is consistence on my part. If I tolerate the whining one time and not the next, he isn't going to understand and assume, rightfully so, that his behavior can be any way he wants it to be. He's learning about boundaries, what he can and can't do, both physically and socially, and if he doesn't learn this now it's going to be harder for him to learn later.
Hang in there, I know it's hard. Just remember, YOU'RE the mom, and YOU set the tone for her behavior. {{HUGS}}
And I'm sorry this is SO long!