I think his dad has actually already accepted Tsugumi but he’s just tsundere and prideful.
Tsugumi is fighting for his love compromising accommodating and everyone around him sees that including Megumis dad but as a doting tsundere and formerly prejudiced Alpha he wants to make sure his kid isn’t just rushing into things which I think he is slowly realizing ie Tsugumi being calm and Megumi taking responsibility over his Omega etc
He standing on business about his lmao as he should because that guy is really out of line