What is ironic about huck's decision to go back and allow the widow to civilize him?

Huck simply isn't the type to be "civilized" in the way that the widow Douglas wants him to be. Dressing nicely, reading the Bible and going to school is the opposite of what Huck's free spirit wants him to do. The irony is painfully obvious as Huck attempts to appease the Widow but alas, Huck does run away and the adventure begins!

Huck's decision to go back to the Widow is ironic because of his rationale for doing it. Far from wanting to genuinely become a "civilized" member of society, Huck goes back to the Widow because Tom Sawyer told him that he would hire him to be a part of his "robber" gang.

Good point Roskolnikov, Huck certainly does go to the Widow's place in order to facilitate his wilder spirit in Tom's new gang.