Hi Bailey, welcome to Global Paw!
In my opinion, the best way to stop Delilah from annoying her big brother is to distract her before she gets the chance to do so. Try offering Delilah something that is more exciting. I would suggest that when you see her going over to BJ, get her attention as quickly as you can with a food treat, toy or just acting silly and excited. She needs to learn that being around BJ does not mean she has to be all over him all the time. If you can make yourself more exciting to her, hopefully she'll come and pester you, and she'll stop pestering BJ.