"That way he could have spent more time with Yui"
This kind of implies her dad is dead, and not that he just left. If he just left them, Saeko giving birth earlier doesn't stop him from leaving her just as early. But it's too early to make conclusions.
It is clear that this isn't going to be a comfy read at any point given how crazy Saeko is for her daughter, but color me interested. This setup has dumpster fire potential. I'm just concerned that Yui is likely to get bullied at school, and is all the more likely because that creates a reason for Saeko to go on a rampage...