These are not sentences, just sentence fragments. You'll need more words to make a complete sentence.
I think you want "A mother asked her little son [to help her wash the dishes]", as Clive suggested. "asked to" doesn't work. "asked of" means something different and would not typically be used in that way. "asked of" suggests imposing upon someone in an important way.
Superb explanation. The complete sentence is like this.
"Why can't you be like the Happy Prince?" asked a sensible mother of her little boy who was crying for the moon. "The Happy Prince never dreams of crying for anything."
I think you could use literary analysis. She may "ask of" as "wanting from him to be like the Prince" (maybe the first quoted line "Why can't you... is something between a thought and an active voice).
Sorry for not being so clear, but I am not a native speaker, nor a linguist.