Hello and Thank You for using Just Answer. I am sorry to hear about the difficulties that you are experiencing that your grandson and his mother and brother. If needed, you may have your grandchild let his pediatrician be aware of his behavior and have an assessment of your grandson. In your the meantime, he is basically asserting his independence and wants things his way. There is no way your grandson's mother should be disrespectful to his mother in no way, shape , or form. The mom is the authority figure, The mom( and dad} need to establish boundaries and stick to established rules and consequences.
See if you can get the grandson to improve his behavior. Start focusing on the times that he is good and respectful. Do not concentrate on the disobedience so much unless he is causing danger to someone else. Tell your grandson that he is going to receive a sticker every time he behaves. It can be morning, afternoon, and night. Or it can be once a day. When he behaves week, he gets a sticker on a calendar or on a chart. After ten to 15 stickers, ( you decide) your grandson will receive a little treat of going to the park or beach or a friends house. Whatever he really likes should be his reward. If he does not behave in a positive well, he does not receive any sticker.
The goal is to teach your grandson to be responsible for his own actions and to realize that he needs to change his actions. No need to yell or tell him more than once to obey. Do not give him attention that he is accustomed to when he misbehaves. Really reward him EVERY time when he behaves well. Try this for a few months. It will take a time but he can change his ways if you are patient and consistent.
Have a good day.