Fwiw, the daughter hasn't gone back on her word yet. Koto's still got one person caring for her, so the promise to be a friend when Koto's all alone still holds.
But seriously, when a parent has been lost, the kids kinda need to accept that the remaining parent isn't going to put their love life permanently on hold. He may have picked the wrong person, but I get the feeling his daughter would be throwing this fit even if he picked the coworker. Miya wants attention, but on her terms. The way she's acting now, Miya wouldn't ever accept a step-mother, even when she's older.