You are sweet to have such care and concern. What you report is normal behavior, however frustrating it is.
But that doesn't mean everyone needs to sit back and let her rule the house. So, let's go back to basics. 1-We need to ignore this behavior a lot more than is happening now. she is learning that she gets more attention by acting this way as you mention when she smiles as she is being told that her behavior is unacceptable. When she begins to act out at home, I would completely ignore the behavior unless of course she is in danger of hurting herself or one of the other children. Se has learned that this behavior gets a reaction. Turn and walk away...no talking no nothing.
2-The eating is the same thing...more attention is given. Put on her plate what is made for the meal...she either eats it or she doesn't and the parents do not become short order cooks and continue to prepare other things in the hope that she will eat. If she is hungry she will eat. The parents can say once...this is what is for dinner it is your choice to eat it or not, but you will not be given anything else.
3-Consistency is the key here. No wiggle room. set the boundary whatever works and then stick to it.
4-Let her know of the rules so that it is clear to her. Such as, it is time to brush your teeth. If she begins fussing you say, you need to brush your teeth now and if you don't you will lose play time with her favorite dolly. If she does not respond go and get her favorite dolly and put it away in the closet.
5-Thse new boundaries WILL be met with screaming and protest and for the first few days until she gets used to the consistency she will act out more to try to get everyone's attention around it. remain calm and stik to the plan and the boundaries.
6-Give her some area where she can "win" kids need this so that they can feel in control of some things. The things that aren't such a big deal let her "get away" with some things. but when it is time to follow the important things remain firm.
Let me know how you feel about this.