As BigBadBarry wrote:
"If she works nights then she should sleep in the day! And if she can sleep through a baby screaming then she is in the wrong profession"
How old is your baby? I don't think you said?
A tiny baby rolling is surprising. DS was a very early roller at 12 weeks (somewhat annoyingly!), and no other baby I know rolled until 4-6 months.
If your DS2 is under that age, it seems more likely that after hours of soothing a crying baby the night nanny put him down on his tummy so he'd settle and she could sleep.
Don't quite understand the money, as it was a present to you? But I'd be getting a refund for any days left and using that on another night nanny who is of a higher standard.
I probably wouldn't have refused to pay for last night, but only paid until 4/5am, whenever she stopped doing her job, or a little less due to the unprofessional behaviour. Either she hadn't been prepared to do a night job, which is rubbish to then expect to be able to do the job in the first place, and / or she laid the baby on her stomach against all SIDS advice, which is shockingly bad behaviour as well.
Either way, you hired her to do a job, which she didn't do. She has broken your trust and proved herself unreliable as well. You are trusting her with the most precious and vulnerable thing in your life. A great deal of trust is needed otherwise how would you be able to sleep if you had to be vigilant each time you heard a squeak and waited to hear if she'd responded appropriately.
How crap, and I'm sorry you now have no help when you'd anticipated a few more nights, and probably had planned around getting those full nights sleep.