First hatchling today, HELP needed

I have quite similar problems with my buttons, the mother leaving her clutch the moment she gets one or two chicks out of say 5-6 eggs or so. With that case, since I have an incubator, I just put them in there, but that can lead to them being unfamilar with their real mother. I tried putting them in with their mother after hatching in the incubator and most times the babies wont recognise her as "mum", other times it just works out fine. Spose you just have to be lucky with how it ends up. 

Is she a first time mother? A few of my hens had to go through a clutch before they got it right....sometimes the fathers are the better parents as well. Is there a male with your hen? It's good to leave him with the chicks/mother if he is docile natured. I find they brood the chicks more often then the hens do, and he will feed them etc. Other males may kill them a week or so after hatching (a problem with one male I own, otherwise I've been lucky with the males being good daddies).

I wouldnt remove the baby from the mother, but perhaps bring the birds indoors where it's warmer, or add a heat lamp inside the cage so that even if the mother wont sit on them, the baby will head straight for the source of warmth by itself. They can become troublesome to handraise, especially if you have other commitments such as work or school. It is best to let the mother raise her own chick.

Hope you are having luck with your quails.