How do I change pets away from a stable?

I can see and manipulate my pets and mounts at a stable, but my “Appearances” window doesn’t seem to be working. The “Mounts” tab says I have “Total Mounts: 11”, but only shows me 5. The “Pet Journal” tab says “Total Pets: 0”, but in the stable I have 5 different kinds of pets I’ve collected. How do I manage my pets and mounts?