I am deeply sorry to hear about your wife's health problem at the moment.
And sincerely hope that it will not be as serious as it sounds.
Spitting blood could be also down to TB, and it is, as far as I am aware, treatable.
As per paying the hospital bills, I am afraid I haven't a clue to which way is best.
I understand your reluctance to send any money to the family, but I reckon that it is the only option open at the moment.
The problem in Phil is that everything is paid upfront...
You have to pay for the prescription, take it to the chemist/pharmacist and pay for it... Then take said medicines to the doctor for him/her to administer.
And Phil hospitals are known in not releasing the patient, until the bill is paid up.
Ideally you should try to email the hospital admin by email with the relevant details at hand and offer to send the money directly to them, or the cash to your good lady.
www.xoom.com is very good and reliable, they can pay your deposit to an existing bank account, or better they can deliver the cash directly to the person in question, provided some ID is present.
Try xoom. I been using it for a few years, and haven't had any problems with it. And if you already have a paypal account, it will be easier to set up, as they will take the funds from paypal. and paypal gets them off your bank account.
Good luck, and all the best to your wife and yourself.