How to make the game randomly generate certain types of townies/household?

Is there a certain way to make the game generate certain types of townies? For example a married couple with or without children, single father, family with female child, family with male teen, etc.

I only have base game, and currently playing with auto age off for unplayed household. I noticed that when the game generates a family, it always a family of single mother with female teen and a male child. And only one randomly generated family that consist of a married couple with male child, and I don’t know what the trigger for it.

I tried to go to park or playgrounds a few times, erasing the household that I do not want, to make the game to generate new family with kids,  but it always generate a household of single mother, female teen, and male child. I have never seen the opposite type nor any new family of married couple with children again.

I am playing on a new save and trying a new gameplay ideas where I mostly control one family and only age up other premade/randomly generated family when I decided to marry a sim from those household. I’m not sure if this is another known issue, but my sims has been giving birth to male babies only for around 5 generations, and I wanted to have a story where my heir marry their BFF from childhood but could not as I could not make the game randomly generate a family with female child, so I just wait until they age up to teen to choose their lifetime partner.

I know that there are mods that help to create various type of household but I don’t want to rely on mods. So I would like to know if there a ways to trigger the game to generate certain types of townies.

Below are what I noticed from my own observations on how to trigger certain types of sims. 
Going to park or playgrounds: generate family of single mother with female teen and male child. 
Going to bar in Oasis Springs: generate female young adults bar regulars. 
Going to lot with Teen neighborhood trait: Generate single teen (male or female) household (no parents)

But I noticed my game have a few single males and females unemployed young adult sims, so I would like to know if there are other triggers to generate those, especially household of married couples, single father and household with female child. Please advise. Thank you.