Help save Nijinska

Nijiska is our little adored 7 years old rescue cat and since last year she has been suffering with stone in the gallbladder. So far we have managed to cure her with a session of medicines every 4/5 months but since the condition has become chronic and is deteriorating her liver with potential fatal consequences she is unfortunately in need of a operation asap to entirely remove the gallbladder. The alternative is to euthanize our cat, as the health care system here, even for pet, is too expensive.
I rescued Nijiska from a NYC rescue organization in March 2014. She was the runt of a litter and beyond adorable. She lived with me in many places in Brooklyn, traveled on endless weekend trips with my partner Chris and I and she has now become our daughter Neema's favorite friend. She means the world to us and we could not imagine our family without her presence. 
Unfortunately our pet insurance does not want to cover the expenses as they claim it is a precondition. For us this is not a little cost as childcare in NYC is also impossibly expensive so we are asking for some help. Any dollar count towards getting our other baby back on her feet! Estimate of $4500  would include vet's exam, x-rays, blood work, possible ultrasound, feeding tube placement, and potentially 3 days in hospital. This is a HUGE surgery: they can have post operative and intra-operative complications.  They can become septic. Hence why the price is so high. This is not a simple spay removal and it's not typically a common surgery for general practice but once through recovery they tend to do ok which is what I am sure will happen to our cat.
Thank you so much in advance for any help you can offer!