I love the names you have chosen for your boys.
very cute
I had the same problems with my girls when we added Cooper. She was hyper and ready to play while Maddie acted like she couldn't be in the same room with her Cooper was about 15 weeks and Maddie was closer to 2 years.
I did what you are already doing. ~Took them outside together~Took Maddie on her own special bye-bye trips whenever possible~Kept her in the bed with us as she was used to, Cooper stayed in her crate~ALWAYS fed and gave Maddie treats first~Made sure to make contact or greet Maddie first when I came in~Made sure she had areas of escape she could get to and Cooper was not allowed.
It took a month or so before they actually played together. What a beautiful moment that was too.
Keep doing what you're doing and I am sure your Dudley will come around. He will realize he is not being replaced and his life is not going to change, only get better with a brother.