Only your mother can be involved in this decision. Only the hospital can work out a payment schedule. I've never heard of a hospital being willing to accept payments for a non-life-threatening procedure. This is considered cosmetic surgery, except for certain cases. If they won't accept a payment schedule from your mom, she needs to put it in a savings account and be prepared to pay at the time of surgery.
However, I was given a full scholarship for my surgery in exchange for being in a 7-year study. But I went to a university hospital for my procedure, not a private hospital.
See your hospital's ombudsman and ask if there are alternatives.