This is what Im thinking - a) mom is lying or b) she hasn't been around enough kids for mom to even know that she is like this!
I agree with what you're saying..she is not used to being in a daycare setting and the fact that she's been there a month but sick for two of the weeks means it's way too eary to expect "normal" behaviour. You're lucky if you have a 2yr old sit for a whole story let alone a one year old!Ignore her as long as she's not hurting anyone...she'll come around when she isn't getting your constant attention. Since she's awake so early is she having a morning nap? I would make sure she naps at around 8-9am for about 30-45min...that should help! 5:45am - noon is quite a long stretch without a nap.
Now the biting & hitting isn't allowed - I would also do the playpen thing but it'll take a few days to "kick-in" oh and if you have a lot of free-play she might be bored. Keep her busy with new things and her attention will be focused on that rather than what the other kids are doing/touching.