How would you say to a crazy neighbor when she asks why your kids can't come...

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I have a new neighbor who has a child around the same age as mine. Before she even physically moved in she was at my door being pushy. When I open the door she'll do things like stick her head in my doorway or leave little space in between the two of us, as if she wants to push her way in. She's given me a hug, a kiss and runs her mouth a little too much. She comes to my door, or sends her son, almost every single day sometimes more than once. If my kids say that they will be down in a minute, within a few minutes they're might be back knocking at the door. This and other behavior makes me wonder about her mental health. She's begged my child to come down. My child took a little while to get down there. But, when she did neighbor says "Oh, it's too late. I gotta go to bed, now. I'm sick. Bye,honey." and, then closed the door in my childs face - not even making sure that she made it up the stairs safely at 5 y.o. Two seconds later she's screaming at my child to come back because she thought that it was later than it actually was. Another day, her son was at my house for a while and then he went down to his own house. My children followed. One of my children was let in, the other was not. The mother then came to the door and said "Aaron said you hit him. He don't want you in here." in a serious tone. My child hisself, but I didn't like her tone. Then, later on, one of my children came home without the other. Turns out that my child and her child were nagging each other and she couldn't take my child's whining so she sent her back upstairs. Then, later that night, while all of my children are sleeping accept for my little two year old, she screams into the hallway - as loud as she can - "Go to Bed!!!" and slams the door. I'm not allowing my children down there anymore. Her child can come up, but she's a bit too unstable for my children to be around. What would you say if confronted by the neighbor?