A A Milne
Are you sure you've got the right one? I may be wrong but IIRC it was Shepherd (Wind in the Willows) who had a difficult relationship with his son. Milne didn't until long after the Pooh episode. Milne stopped writing children's books because he was worried about the effect on his son, but it was much later before the son became estranged. The confusion may arise because Milne did a well known theatrical adaptation of Wind in the Willows (Toad of Toad Hall).
Milne was invalided out of WW1 but stayed in the Army in a desk role (writing propaganda) till after the war and subsequently became very anti-war for a while, evidence of his bad judgement being an attack of pacifism in 1934.
But someone more obsessive about Punch and Milne than I may be able to correct me. I'd like to know.