I think eunyeong was lying about clothes and lending money. Because his mom always believed only in what she thinks is happening anyway. So he was a bit silly, a bit spiteful.
And I was wrong about eunyeong frustrated that she gave the money to the dad. Actually, it seems like he "bought" his freedom from them. What a pair of "parents"... :/
I feel like Eunyung like a normal kid still feels sympathy towards his mother deep inside. Maybe he was secretly giving money only to her hoping she would left her husband eventually. But instead she shared these heavy-earned money with the person Eunyung hates. I think that's what got him the most. I also don't think she makes it on purpose to provoke Eunyung. It's probably just the way she was raised in her times, plus her personality. Some old wives sincerely believe they're stuck with their husbands and have to "take care of the home".
I don't understand why these two are together. They're constantly uncomfortable with each other, so what's the point.