AM-1, at ~120 kpc, and Pal 14, at ~70 kpc, are two of the most distant Galactic globular clusters known. We present Hubble Space Telescope WFPC2 photometry of AM-1 and Pal 14 that reveals unprecedented depth and detail in the color-magnitude diagrams of these two clusters. Absolute and relative age measurements confirm that both are younger than the inner halo globular cluster M 3 by 1.5-2 Gyr, assuming all three clusters have similar compositions. Thus AM-1 and Pal 14 join Pal 3, Pal 4, and Eridanus (studied by Stetson et al.) as distant Galactic globular clusters with red horizontal branches and young ages relative to the inner halo. Within the context of the entire body of research on the ages of second parameter globular clusters, the observed correlation between age and horizontal branch morphology suggests that age is the best candidate for the second parameter. However, this conclusion is tempered by the lack of precise chemical abundance determinations for a significant fraction of second parameter globular clusters.