Hi AmitC,
Please try to submit it to the ESIC hospital and see what happens.
You have to submit a reimbursement claim bill/bills as an IP. Write an application to the Administrative Medical Officer, ESI Scheme, in the place of treatment had through the concerned Insurance Medical Officer in charge, ESI Scheme Dispensary allotted to the employee along with the claim bill format available at the Dispensary. They have to mention the cause of diseases and the reason for diverting to a Pvt. hospital.
Did you get the prior approval before admitting your wife to a Pvt. hospital? Is this private hospital among the list recognized as a referral hospital by the ESI hospital for such treatment? Was this an emergency or not? It is better to approach the concerned Medical Officer/office for proper guidance on how to apply for reimbursement in the form.
Also, go through the stipulations/regulations for 'reimbursement of claims' referenced in ESIC.