This is a great question to think about, because Leonato seems to present two paradoxical impressions in terms of his relationship with his one and only child, Hero. In the infamous marriage scene of Act IV scene 1, for example, he openly states that he wishes his daughter were dead, even going as far to say that he hopes she is dead when she faints in shock and terror. Certainly the harshness of his words and the way that he responds to her public shaming severely limits our impressions of him as a good father to Hero. However, I would point you towards Act V scene 1, where we see a very different side of Leonato. As he is talking to his brother, he expresses his grief and his sadness at what has happened to his daughter. He says:
My griefs cry louder than advertisement.
In addition he states that in his "soul" he knows that Hero was "belied," and in response to his brother's insistence that he lay aside his grief, points out the futile nature of counsel at such times:
For, brother, men
Can counsel and speak comfort to that grief
Which they themselves not feel. But tasting it,
Their counsel turns to passion, which before
Would give preceptial medicine to rage,
Fetter strong madness in a silken thread,
Charm ache with air and agony with words.
The Leonato that we see in this scene, therefore, is very different from the Leonato that we saw in Act IV scene 1. Perhaps the difference can be explained by the passing of time and the way that has helped Leonato look upon the situation with mature reflection. Either way, he is presented in this scene as a loving father who is overwhelmed with grief at the wrong that has been done to his daughter and willing to fight for her honour.