There is a definite sense in which both Lear and Edgar are linked as characters in the play. Note how during the storm, Edgar ends up in the same shelter as Lear and the Fool. He also appears to be mad, but through a calculated choice to protect himself and to be overlooked. Of course, starting with Edgar, there is a sense in which he suffers for the way in which his father is taken in by the plot of Edmund to disinherit his half-brother and take his place in his father's affections. Gloucester's readiness to believe Edmund and to disinherit his true son, Edgar, parallels Lear's willingness to do the same to Cordelia, his one true daughter who he loves. Edgar therefore could be said to suffer for the sins of his father, but Edgar, throughout the play, shows a resilience that ends up in his restoration as the heir of his son and one of the few characters that survives. I personally would argue that Gloucester suffers for his own sins more than his son does.
Again, your statement concerning Lear is problematic. He does indeed suffer because of the sins of Regan and Goneril because of their abuse of the power they have received from him, but I would argue that this suffering stems from his own foolishness and the way that he has chosen to prize appearances above reality. When we meet him we see that he wants the trappings of power and the ability to enjoy himself without the responsibility and care for his subjects. It is highly telling therefore that Lear says to his daughters "Which of you shall we say doth love us most" rather than "Which of you doth love us most." Appearance is what Lear is after, not reality, and appearance is certainly what he receives in the insincere protestations of love from Regan and Goneril. In spite of his love for Cordelia, he is unable to see the reality in her words. Yes, there is a sense in which Lear suffers because of the sins of his daughters, but I would argue he actually suffers more because of his own sins.