In 63:1-6 we see an amazingly strong picture of a majestic person who alone speaks in righteousness, is mighty to save, is strong enough to walk that road alone, and is powerful enough to execute vengeance with powerful wrath. It's an awesome picture of the Lord. In 7-9 we see Isaiah talking of the Lord's goodness to the people of Israel, His calling of them as His people and His role as Savior toward them. Starting in verse 10, Isaiah recounts Israel's rebellion against the Lord (with mention of the Holy Spirit) and the process of Him then fighting against His own people to bring them back and remind them of how mightily the Lord worked in and among them for their good and especially for the sake of His glorious name (14). Verses 15-19 seem like other nations talking to God about their own relationship to God and Israel's as well. Verse 16 seems to say that the "voice" is not Isaiah or one of Israel's people, but someone outside God's chosen people. Either that or the speaker is referring to how their own behavior is as though they never knew the Lord and have never been ruled by Him. The speaker proclaims that the Lord IS his Father and Redeemer, though he and his people have been caused to stray and have hard hearts by the Lord Himself (16-17). This is certainly connected to their rebellion from verse 10.
62:1-6 screams "Jesus!" to me, and it's terrifyingly strong. He is both mighty to save and mighty to execute vengeance against the evil. He brings redemption AND wrath. In 63 we see the same double-edged sword of God's loving kindness. God chooses and protects His people, but when their rebellion against the Lord rejects the blessings of provision that He has given them, the Lord Himself afflicts them, hardens their hearts in keeping with their rebellion, and fights against them. In essence, as the people of God's own choosing, they become unrecognizable as those called by His name and blessed for the sake of His own glory. It's a sad and cautionary tale for us all.