Will it be a problem for the person that provided surety?

The advise rendered by Mr. Sivaramprasad Kappagantu can be the best option available before you instead of getting confused over different kinds of opinions from different people either from this forum or elsewhere.

Your wife's lawyer will be having proper answers to your questions hence be in touch with him. 

SO it mans that with irresponsible father-in-law you cannot contest case successfully in Delhi.  You should either engage good lawyer, your wife to apply for examption to attend  and permisssion to be in USA.  If such permission is refused she should remain in India throghout the case (may be 2,5,8,15 or more years).  It is only a person well versed with the facts of the case who can advise whether the case is fit enought to apply to High Court for quashing of FIR.

or else she can seek mercy of opposite party to drop her name.

Thanks to all of you for your time and suggesitons.  Discussions are in progress with lawyers and hoping it will be resolved soon with blessings of god.