Well…. the first chick is still fine?  Mama is treating it well?  If the one that was hatching took a long rest in the middle, (as they often do), or else it died in the process, (which could have happened too) and mama looked in at it and freaked out, she may have cleaned up the remains, or even actually killed it.  A bit ugly I know, but they have an instinct to keep the nest clean of all dead (or perceived dead/dying) chicks to protect the live ones from predators who would be attracted by the scent.

…since this is her first, she's probably not sure of everything herself.

Either way, without an incubator you're a bit stuck.  If you were to remove eggs now, the balance of humidity and heat would be pretty messed up.  Humidity is the big problem, you could approximate the heat with a simple light bulb in a box at this point, but with too dry an environment, the membrane around the chick could/would shrink once the process starts, and 'heat shrink' around the chick which suffocates them.

All I can suggest is keep as close an eye on her as possible.  If the chicks seem in danger you can take them away and try to do it.  Warning not to 'help' the chick out though, that usually leads to serious bleeding by the chick. They do take long breaks in this process, hours at a time, even 10, 12, or 20 hours!

I KNOW!!  It's so crazy! As if the stress of setting on a nest weren't bad enough for them!  Hopefully the heat will have eased by the time they're ready to hatch!

Something you can do to get her to take chicks after she's 'done' is wait till it's pitch dark outside, go out with the tiniest flashlight you can manage to get by with, or drape a bigger one with a cloth if you need to, and slip the chicks under her while she's asleep.  They usually just shift around and make room, then they're there when they all wake up in the morning and she doesn't have a clue that there's anything new going on.

That whole 'touch a baby bird and the mother will smell you' and reject them thing is a total myth. The only bird with a sense of smell to speak of are vultures.  The rest have no real sense of smell and they don't call them 'bird brains' for no reason at all, they can't count and have NO IDEA how big their clutch of chics is!!!  Usually they wake up, the chicks are there, so they take care of them. 

Chickens really are very addicting. If anyone is building a chicken coop, be sure to build it much bigger than you think you need it… you'll always want more!

I'm sorry I didn't see your question earlier Butterbean but with an Ameraucana rooster, and Dominiker hens, they'll be a cross, not either or.  Just like if a beagle an a poodle had pups…  The thing with chickens is, there's no formal tracking of crosses, if you have a hen or a roo that fits the "American Standard of Perfection"  for the breed, you can call it that breed, though it would be unethical untill you have proven at least to yourself, that it breeds true with several clutches of chicks, and probably several generations after that too.  Any time a bird is sold as being one of any certain breed people want to be able to count on any chicks hatched from two birds of that same breed (including your cross I mean) will produce chicks that are at least decent examples of that breed.

See, the first generation of that cross may look like say, the Dominiker, but if one of those chicks is bred to another Dominker roo, they may actually produce chicks that wind up looking oddly like the Ameraucana grandsire.  Genetics are such an odd thing!

I hope that made sense!