Struggling to find the episode in particular because it was a scene with Eustace's mother where she was abusive and it mimmicks the same style as Eustace has towards Courage. If anyone knows, let Messofanego know. If I remember I'll quote again.
It may possibly be "Mother's Day" but I'm not certain and can't really watch it right now to be sure (saw it a long time ago). From Google the episode synopsis seems to point to it. "Eustace visits his mother for Mother's Day with Courage. Though Eustace tries to win his mother's love, she would rather dote on Courage, much to the master's envy and the pet's dismay."
Otherwise you may need to binge watch all of Courage.
The thing is I really recall an episode right now as well that dives more into Eustace's past. In my mini-marathon yesterday I saw Mother's Day and that isn't quite it. The episode just shows how Ma Bagge's likes Courage more than Eustace, and criticizes and gives a hard time to Eustace, but they don't go into their past together.
I think what I and you are thinking of though is a collection of episodes though. The more I'm thinking right now, the more I'm pretty sure there isn't an episode dedicated to Eustace's back-story, rather than flashes to his younger years showing how shitty his family was to him growing up in a number of different episodes briefly. An example of this is I believe each season of the show has an episode where the plot has something to do with Eustace's long-dead but super adventurous, successful, manly brother, and each time one of his episodes comes along it sheds a bit more light on the relationship the two of them had. In the brother's final episode, which is the hunting episode with the deer in Season 4 I believe, we see a full-on flashback (I believe for the first time rather than just talked about with his picture as the focus), where Eustace wants to go hunting with his 'cool older brother', but his brother undermines Eustace as his 'girly' younger brother (being a macho man type), and keep on calling Eustace 'Useless' in place of his name, which really upsets him and is shown the nickname still really upsets him to this day.
I don't remember exactly, but I think the same thing happens with Ma Bagge's, as I recall her having character development through the series (a notable example being she adores Courage at the start of the series, but by the end of it she ends up hating Courage more than she hates Eustace and Muriel), I think Eustace's relationship with his mother was shown like this slowly.
I think the first episode where Eustace talks about his childhood is the episode that Eustace's mother tries to use the ghost with a grudge against Muriel's family linage to split Eustace and Muriel up, and Courage acts as a marriage therapist for the two of them, and Eustace talks about how his mom never liked him.
