Such backyard dramas can be frustrating, especially when there is no obvious way to affect the outcome.

When you saw five squirrel rush up the juniper, chances are they weren't bent on raiding the nest. We guess you might have observed a squirrelish dispute of some kind that just happened to culminate in the vicinity of the nest.

Whether any of the squirrels eventually returns specifically to disturb the nest remains to be seen.  If/when that happens they probably won't be returning as a group.

We don't know whether and how pepper might be used to deter squirrels in the circumstances you have described.  

The experts don't have much to say that will help either:
https://www.allaboutbirds.org/news/how-can-i-protect-the-baby-birds-in-a-nest-from-predatory-birds-and-other-predators-like-snakes-and-cats/