Yes, en refers to ton père. Generally speaking, the pronoun en stands for de + noun. See When to use the pronoun en? for a general introduction to pronouns and prepositions.

Here it would be possible to use either sa or en:

Tu n’as pas la dignité de ton père.
Tu n’as pas sa dignité.
Tu n’en as pas la dignité.

The meaning is roughly the same, but there is a subtle distinction. Using sa suggests that the father’s dignity may have been transmitted to the child, whereas using en merely suggests a similar dignity. However, this nuance is rather weak; it would perfectly possible to say “sa dignité” even if the people involved were not related and there was no suggestion that the quality was transmitted.