The bit of divinity left behind is for her to maintain her own form.
Anyway, Kamiyagawa had already communicated with Sister Kaku over there. The God Artisan said as long as the "Demon God Umbilical Cord" was infused with the power of the Ghost Mother Goddess, that would work. That umbilical cord contained both divine blood and divinity, nourishing each other, making it a perfect material for shrine construction in the hands of a master artisan.
As for the weakened Demon Child Mother, she'd been recuperating in her shrine lately.
That shrine, although dilapidated, is still a bona fide Ghost Mother Goddess Shrine. The faith power for her in the Present World can indeed be channeled into the shrine.
Besides, Kamiyagawa would often come by Kawahara Cemetery to light a Soul-calming Candle for her.
So, for the Demon Child Mother, it's just a matter of time before she regains her strength. But when she recovers, her strength as an Arajin will probably have taken a serious hit.