I don't think the hardness of an animated object would stack with the DR from the template. Isn't hardness 10 treated equivalently to DR 10/-?
As an analogy, consider putting Stoneskin on a 20th-level barbarian. Innately, he has DR 4/-; the spell grants DR 10/+5. Against someone with a +5 weapon he would have DR 4, while against anyone else he would have DR 10 (not 14). Am I right?
So if a thing already has hardness 10, adding DR 10/+3 would be pointless; it would still reduce all damage by 10.
As an analogy, consider putting Stoneskin on a 20th-level barbarian. Innately, he has DR 4/-; the spell grants DR 10/+5. Against someone with a +5 weapon he would have DR 4, while against anyone else he would have DR 10 (not 14). Am I right?
So if a thing already has hardness 10, adding DR 10/+3 would be pointless; it would still reduce all damage by 10.