Please try to submit it to the ESIC hospital and see what happens.
Submitting a Reimbursement Claim
You have to submit a reimbursement claim bill as an IP. Write an application to the Administrative Medical Officer, ESI Scheme, in the place of treatment 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 the diseases and the reason for diverting to a private hospital.
Important Considerations
Did you get prior approval before admitting your wife to a private 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.