How do i convince my mom to let me get another dog?

I think you, and every other kid on YA who asks this, need to realize that your mom is saying no for a reason. If your GSP is lonely, play with her more and talk her for long walks every day. Get her some toys that stimulate her mind, like Kong ones with treats in it. If your mom says no, it will stay as no. Personally I think it's kind of unkind to leave a dog outside by itself, so you would be better to convince your mom to keep the dog inside with you rather than locked outside.