Conversation so far:
Who was Honecker's father?
CANNOTANSWER.
Did Honecker marry?
Honecker was married three times.
Who was his 1st wife?
he married the prison warden Charlotte Schanuel.
Who was his 2nd wife?
By the time of her death, Honecker was already romantically involved with the Free German Youth official Edith Baumann.
Who was his 3rd wife?
Following his divorce and reportedly under pressure from the Politburo, he married Feist.
Why was he under pressure from Politburo and/or what does that have to do with remarrying?
political reasons.

Question: Why did he divorce his second wife?
Self-contained rewrite: Why did Erich Honecker divorce his second wife?