Hi Kelly, 

I would recommend that you remove the galled sections of your cedar and any infected apples, but removing the whole cedar tree isn't guaranteed to help. Unfortunately, these fungal spores can blow into your apples from up to several miles away. Even without this cedar, it is possible you will continue to see cedar-apple rust. However, removing this major source of nearby inoculum will definitely help!

I would then try to dry out these branches as far from your apples as possible on your property and fully remove them if possible. 

While infected apple tissue cannot be recovered, fungicides can be applied to limit spread this year and to prevent disease occurrence next year. The fungicide myclobutanil (Immunox) would be a good choice here. This would have to be applied every 7 days from flowering until the juniper galls fully dry up to prevent cedar-apple rust on your apples. 

Here's an article with more information: Cedar-Apple Rust | Ohioline (osu.edu)