What are the characters of the two fathers, Lear and Gloucester, and the mistakes of judgement they make?
Both fathers are arrogant and blind to their children.
Gloucester's attitude toward his children is established in the first scene when he brags about how much fun he had in begetting Edmond, his illegitimate son, while the young man is standing right there. He treats him like a lap dog.
It is amazing how quickly he believes Edmond's lies about Edgar. Admittedly, Edmond sells his brother's "betrayal" but shouldn't a father know his children better? The deception of Edmond is perhaps understandable since he is away at school most of the time and has spent very little time with Gloucester.
Edgar, on the other hand, would appear to be the apple of daddy's eye. He remains faithful to his father despite having to flee and disguise himself. He is there for his father when the old man needs him the most. Once Gloucester is blind, he begins to see.
King Lear's question in Act I, scene 1 is also telling. It shows that the old king is blind to the truth. Are Goneril and Regan evil? I don't think so. They haven't lived under daddy's roof for quite some time. Each woman has her own life with her husband away from their father. Do they love him? I'm sure they do but as a daughter should love her father. They tell Lear what he wants to hear. They know him well enough to know he wants his ego stroked.
In her innocence, Cordelia does not know what to say since she cannot heave her heart into her mouth. Lear obviously does not under what love truly is since he feels the need to ask the question and does not understand that love is expansive.
For their part, Goneril and Regan feel that they must protect themselves against the whims of their father. If he could disown his favorite daughter and exile Kent just because they did not please him, what would he do to them if they displease him? When people are scared, rational behavior disappears.
As Lear loses his identity beginning with the loss of his crown, then his men, he, too, experiences fear.
Just as Edgar and Gloucester are reunited, so, too, are Cordelia and Lear. Before they die, each father realizes who truly loves them and how powerful that love is.