As you said," I requested her father for mutual divorce but he declined.Her family is doing her 2nd marriage quickly."
The only quick solution is Divorce by mutual consent.i dont understand why her family member declined as they have to doing her second marriage quickly ,first they have to file Divorce by mutual consent petition under section 13 B of hindu marriage act,1955.If there is no hope for reconciliation ,then Dv by mutual consent is a easy way.
you said," If I file a case of bigamy against her. Can she file false cases like 498A, false dowry charges, against me?"
Why? It will not be valid for your wife to remarry without obtaining divorce from you ,so if she marry then you can file bigamy case but for that wait for that marriage.
Can she file false cases like 498A, false dowry charges, against me?"
Why she want to file as you already said they are in hurry for second marriage.(Her family is doing her 2nd marriage quickly.)
And we cannot measure their mind ,be positive if they file false cases then be brave and ready to fight.
i think you try to reconciliation and if fails try to understand them for dv by mutual consent. otherwise file divorce case.