My guess is, mom will find a new boyfriend or get back together with her old one, ignoring Yuki and dismissing the stuff she said to Yuki (e.g. "You're an adult now, you should be paying for your tuition yourself!")
As for Taiyou, his mom will find out he's dating someone on the next chapter, since he rushed to meet Yuki and also rushed home to greet his mother, so he didn't have enough time to hide evidence. Dunno what will happen next though.