AS about bigamy, she has committed an offence and if u r father can prove about existence of first marriage , marriage stands void. To get marriage to be declared void, he has to file petition in family court. And if she has deserted him for about 4 years, than even in courts of your country, by filing petition father can claim divorce as per provisions of your country as he is citizen in said county.
He can also file a case of cheating as well criminal breach of Trust against her.
As about making paymen of maintainance to my opinion she can claim the same under new law that is domestic violence act wherein a person need not be wife but any lady who resides as that of wife than she is entitle to claim certain benifits as provided under said act including maintainance and residence.
I hope i have thrown light on your querries in case if u still wish to know more on this , may please fwd querry.
Adv ramesh chheda