twinset, you sound like you had it hard when your DD was young, I suppose she may have picked up on a few of your anxieties (as my DD1 did with me, I too had a hard time (not like you though), living far away from family and friends and feeling very very lonely), this probably makes them slightly more highly strung BUT nature is what it is, she was always going to be this way and you have to nurture her to the best you can. As you say, you love her for what she is but it doesn't make it any less easy. I think it always helps if you see you are not the only one who has a child verging on hyperactive!
I find that the summer holiday is the worst for me with DD1 as in it is a constant stream of trying to entertain her along with looking after a large house and 10.5 month baby (as well as being pregnant). I then start to feel ever so slightly resentful towards her as in she will not occupy herself for 5 mins and I can take my frustration out on her by being very sharp and short. We are all human and can only take so much of constantly being mithered(sp?). I am sure they will get easier as they get older.
My main problem with DD1 is that she always has to do the opposite to what you request, if I ask her to get me DD2's bottle, she will say "where, I can't see it?" when it is in front of her. It is a battle of wills more than anything. She enjoys to see people snap in a way. She does it with her best friend.
When you say your DD is being mean, in what way, to you or her peers? My DD can be pretty mean to her best friend and I often wonder how they can be so close. I tell her repeatedly that her behaviour is wrong and she loses privileges if she carries it on but it is like she cannot help it. She is also mean in a very understated way to her sister, she won't give her the time of day, which is quite upsetting. I know when DC3 arrives she will probably transfer her "meanness" to the new baby and be nice to DD2. All very frustrating.
In the 5 mins it has taken me to type this, I was upstairs on the bed on the laptop and DD was downstairs watching Peppa Pig, she has been up 3 times to see if I was still here.
Is your DD a big eater?
Sorry for such a long post - I am glad to talk to someone with a child so like mine!