Conversation so far:
Who was Erich Honecker's father?
Erich Honecker's father was Wilhelm Honecker (1881–1969), a coal miner and political activist.
Did Erich Honecker marry?
Erich Honecker was married three times.
Who was Erich Honecker's 1st wife?
Charlotte Schanuel, née Drost, a.k.a. Lotte Grund
Who was Erich Honecker's 2nd wife?
Edith Baumann (m. 1947; div. 1953).
Who was Erich Honecker's 3rd wife?
Margot Feist (m. 1953; his death 1994; an open relationship acknowledged by the Party, 1952)

Question: Why was he under pressure from Politburo and/or what does that have to do with remarrying?
Self-contained rewrite: Why was Erich Honecker under pressure from Politburo and/or what does that have to do with remarrying?