This manga's lost touch of it's central premise.
Taking care of the kid is not as important and since it's avoiding any kind of romantic interaction like a PLAGUE the character drama actually diverges from the central themes of family.
This is nothing like Gakuen Babysitters, Orange Yane no Chiisana Ie, or Papa no Iu Koto Wo Kikinasai.
The baby's half-demon heritage doesn't cause any challenges for the mom really. The mom having to provide for her child isn't really a challenge she has to face. The child making friends at the park or in a daycare isn't a problem. Like holy crap the premise offers for so many unique and interesting scenarios but it's completely ignored for some dumb music side character schtick.
Just naming those better manga is giving me the urge to reread... I'm gonna have some fun today.