Arsh, your divorce isn't finalized yet so I have no idea how custody works informally until the papers are signed. Perhaps you could agree to what he wants with the condition that once the divorce is finalized you'll be abiding strictly by custody laws.
Arsh when my husband stops calling I know it's because he's in a new relationship with a new woman. It happened three years ago and happened again this year. It was almost identical how he stopped calling and seeing our daughter during both times. When the relationships ended he went back to normal. I think it's honestly think that's one of the better case scenarios if your husband is having an affair - affairs don't usually last. Sure there are stories about affair partners who marry but your husband isn't just any affair partner. He's got two little kids and he's from India where there are customs and traditions that I doubt would honor adultery. So what will your husband say to his family in a few months if he wants to introduce whoever it is after the divorce? Will they really be happy for him and ready to accept another woman knowing how he left you and your daughters? What about people at work? What about his thoughts when he falls asleep at night? At some point he has to face reality. Things won't always be so carefree and fun. It's still really immature and terrible whatever he's doing but I really doubt he's alone going fishing right now. There must be reasons why he's in such a rush to divorce and why he's off traveling so soon after moving out. I think that's good news for you though because this won't last and he'll be back when the affair ends unless he's like my husband and decides one woman isn't enough and keeps going for more.