This is a well-known Nigerian advance fee scam.
Scammers are very good at what they do, and I am sure you want to believe the "daughter" but neither she, her mother, nor the doctor are going to be real. The Nigerians invented this fraud in the first place, and they have raised it to an art form.
The patient would not be admitted to a private hospital in the first place if her expenses weren't covered. And hospitals do not hold people hostage for money.
I do not see a listing for Oba-Adenle Memorial Hospital on any list of Nigerian hospitals. I do not find an official website for such a hospital that can independently corroborate the information you are being fed. The so-called doctor's phone number is ***** mobile phone, according to a reverse international trace. You're not speaking to an office or to a hospital.
You can read the tell tale signs of an advance fee fraud here and see a list of tried and true excuses scammers use to fleece their victims. The hospital scam is on this list.
I know you'd rather believe them than me, but you'd be very unwise to do so. If you wire the $850, they will only ask for more money from you. And more, And more. Until you find out I was right in the first place but by then you'll be out thousands of dollars.
You should not wire any money abroad to someone you have never in your life met based on a so-called emergency. That's always a scam. And if you do, at the very least before you do, you must take steps to independently corroborate that this hospital exists -- good luck with that -- and that this person is a patient in that hospital. By independent corroboration, I mean get the number of the hospital from an official source and not the likely scammer. Then call and ask to speak to the patient.
So I'll be happy to look at any other information you have. If they've sent you any documents, or any photos, you can upload them here with your reply to this question thread.
As I have already told you, a reverse international telephone search tells me that the phone number you have given me is a mobile phone. You can see for yourself here.
It is NOT a hospital number. Of course whoever answered would tell you that Sandra is a patient. You reached one of the scammers!
As far as the hospital is concerned I have found its name on Google too. At the same time, it is only listed on a couple of free listing sites, none of which have a complete address or phone number. It is not listed on any official list of hospitals in Nigeria and official listings are what you need. Anyone can invent the name of a hospital and put them on a free listing site so that it will turn up in a Google search.
I will also add that if this is a private hospital rather than a clinic, they would not admit a patient who is unable to pay the fee.
If you have a photo of this person you can upload with your reply, and some documents and details about her other than this hospital and phone number, I'll be happy to look further. But I stand by my answer having seen this scam many many many times before.
I understand why you'd rather not believe me, in which case you may want to contact the US Embassy in Lagos and have someone there look for the hospital in their phone directory.