Why don’t you have an honest chat with the child and give her a chance? Then when you spend time with her, you can remind her about your conversation and slowly get her to change her ways. It sounds like no one can be bothered with the poor girl and over time, people will dislike her through no fault of her own. Then she’s likely to become worse. Set some special aunty time aside for her and make it a nice day then speak to her while all is calm during that time and at little intervals. He is being stubborn about training so he is clever enough to put the blame back on you. Tell him he did a good cleaning job. A 4-year-old knows that people value cleanliness. Hope he gets the message. Let it sink in a while without apologizing, but find a way to reward his successes with your company.