I think that what Marco is dealing with in his brain is the fact that him being dyslexic meant that he was a disappointment to his father, who probably gave up on him and thus driving Marco from home. He wants to spare his kid that fate.
To that end, Lydia had the same kinda situation - she was in an arranged marriage and couldn't be what she wanted to be, which was being a lesbian. She didn't leave on bad terms with her family but she still misses her family.
I think Marco truly loves Lydia and genuinely wants the relationship with his son he didn't have with his father. And I think Lydia ALSO wants what Marco wants because it would mean she could return home having achieved something that would make both her and her parents happy. Lydia was only turned off the idea of "doing the right thing" because the last time she was likely told about doing the right thing was getting married off (the prudish woman in the caravan also pushed it on her), which she didn't do and hearing Marco say it just dragged up all the things her parents fed her about marrying the boy she was hooked up to.
I think Alfie is totally wrong about Lydia's feelings but Alfie is right that doing what you want is the way to go. The thing is here, Lydia just doesn't realize this is what she wants yet. Lydia thinks she might have to give up this slutty lifestyle with a family but I think the lesson here is that all this fucking around between the two doesn't have to stop just because they have a kid. They can still raise a decent kid and have gratuitous amounts of casual sex with other people.
I don't think this is InCase taking a swing at gender/family roles. He'd be a fucking moron to think that raising a kid alone over having two parents is the better way to go. Thematically the story is building up to say that family is important (as Vera's journey will prove) but family ought not prevent a person from being who they are but there need not be a conflict.