Is the money taken in exchange for dropping the police report, due to the harm inflicted upon the wife and child, considered permissible (halal) or forbidden (haram)?

If the harm that befell the fetus was due to the negligence or dereliction of the female doctor, then she is liable, and the money taken from her is permissible. However, if there was no dereliction on her part, then she is not obligated to anything.

Determining whether the female doctor is liable requires hearing from both parties and an unbiased medical report.

It is permissible, Islamically, to agree with the female doctor on a sum in exchange for waiving the lawsuit; this is called "reconciliation based on denial."