🤣 Although I have a tendency to over-analyze things, it's ironic that I would only skim the surface of something like that. Honestly, it's not much of a spoiler as it is my lack of thinking critically. I felt there was a certain charm to it, but I've been going for the darker potential to what I was looking for rather than the quirkiness that I associate with Usotsuki Lily.

Their uniqueness does affect their relationships, but I was focusing into the relationship itself rather than what created it. Does that make sense?

I like my men androgynous.
I like my women androgynous.

Working Holiday (took a while to find back...) - a man working at a host club one day has a boy claiming to be his son showing up. He tries to reform himself to not be a bad example for him. The boy himself is much more competent at housework than he is, so he takes over the cleaning and cooking.

Cooking Papa - although the father is also a successful businessman, he's also the one doing the cooking at home, because his wife is also a career woman. Well, it's a role-reversal for a traditional country like Japan at least.

Under Prin - action/supernatural type series. The son kind of takes care of his father sometimes.

Seigi no Mikata - this is quite unusual, at least. It centers on the protagonist older sister, who's like the devil in disguise except everything she does earns her the gratitude of people.

Sorry for answering soooo late but a name just popped into my mind:

Oooku - basically an alternate reality where feudal Japan becomes a matriarcal society. I don't want to spoil too much so I won't say more 😛

Thank you Mizura. I haven't read it yet, but I think I'm going to take a liking to Working Holiday. I love the sort of theme in stuff like Ore no Ko desu ka and Aishiteruze Baby where the protagonists, who aren't initially suited for parenthood, grow and become "parents" in a fashion. Not only that, but I take that the child is the mature one.
Cooking Papa is so long! I might have to put this one aside for later. I already have 50 manga/manhwa to tackle down by December. Does the role reversal have an impact on the relationship at hand? Like does he somehow act more submissive to her? That sounds a bit sexist the way I put it. If there is a role reversal, I generally prefer it to be milked for all its worth.
Under Prin Same thing! @.@ The premise sounds really interesting. I might start chugging down manga.
Seigi no Mikata So you're saying that the irony of her actions creates a distorted Hero and Damsel relationship? I'm looking for something a bit more personable. Unless the relationship with her sister flips some relationship cliche. I always thought that she was the typical big mean sister upped to eleven. Again, thank you. I forgot about this manga. I thought it was on my lists, but it wasn't, therefore I skipped over it.

I don't really understand why people feel the need to apologize for answering "late". It's not like a year passed. Also whenever the contribution is made doesn't really matter. It helps people when they're searching or if they're subscribed to a topic. So you're not late, you're just delayed in the collective process. lol. Thank you, funkykiwi. I'm reading Oooku. I forgot to add it to my lists.

At first I was going to debunk it because I wasn't looking for a universal gender reversal. But then I realized that the relationships, even in canon are referred to as a bit odd. Not just the ones involving gender reversal. Thanks again.

I like my men androgynous.
I like my women androgynous.

Cooking Papa doesn't focus that much on his family relationship. It focuses mainly on the cooking, and the fact that the main character is hiding that he's the one doing the cooking from his employees. Everybody thinks it's his wife who does the cooking. Maybe it's not your thing.

As for Seigi no Mikata, it's not so much relationship cliches turned upside down, but extreme distortions between how the younger sister and her family views the older sister, and how everyone else does. Plus the older sister gets married, and well, stuff happens (for example, the husband thinks that the younger sister is crazy about the older sister, whereas in fact she's doing everything -housework etc., so they won't get divorced and the sister won't come home).

Ah, I haven't read this one yet, but maybe you can check it out:
My Mother and the Game-Room Guest

These two are "innocent-looking housewives who are actually gang-boss/ex-troublemaker" situations, not sure if they fit:
Dear, Only You Don't Know!
Mrs Angel

Also, a bit far from topic, but maybe Saint Oniisan. It's Jesus and Buddha coming down to Earth on vacation, and funny situations and puns ensue. It's hilarious. It doesn't really turn around relationship cliches, but at the same time there are few series like it.