Private detective

That is neither illigal nor prohbited, if you feel your daughter is being abused it is better to file complaint against your husband.

Or simply file application to National Commision for Child Protection;

https://ncpcr.gov.in/ebaalnidan/ ;

So as to maintain your matrimonail harmony better to make your husband to be informed of any such steps,if it is complained against him that he abuses the child he will be in big trouble.

If you think your child will be better protected with her real father then hand hover custody to him.

Agree as above, however if you are in delhi then contact;

•  4th & 5th Floor, ISBT Building,
  Kashmere Gate, Delhi -110006
•  011-23862684/91
•  +91-9311551393
•  dcpcr[at]hotmail[dot]com
•  delhichildrightscommission@gamil.com

Just act now to protect your daughter

If your second husband is abusive towards your daughter and harasses you also for this, you may better plan to live separately away from him in order to protect your daughter from suffering any kind of harm from your evil motive husband.

Taking legal actions against him is an action that can be taken later but her safety and protection from his hands is most important.

Take a wise decision at right time