This thread needs some clarification - this situation isn't nearly as clear cut as may seem. So let's go, shall we?
NONE of us on this thread agree with Mom taking off with the kids - that much is clear. But what we think and what India (and to a certain extent the US) thinks are two entirely different things. To wit...
1. As of right now, Mom does have the right to take the children back to India. Remember, we don't have exit controls - we check who's coming in, but not who's leaving. When there's an injunction present, it still doesn't stop her.
2. Just like the US, both parents are required to sign for the minor's Indian passport too...in theory. Unfortunately it's remarkably easy for Mom to lie her way out of the country and take the children with her. India does not have a similar alert program, either.
Read here:
http://passportindia.gov.in/AppOnlineProject/online/faqServicesAvailable
3. (This is where it really goes to hell in a handbasket). Assuming Mom is back in India with the children, Dad is stuck. The Indian courts just won't give custody to either an Indian citizen parent or a US citizen parent if they don't actually live in India. Worse, even if that wasn't the case, Mom has the Golden Uterus.
4. Dad, you're a US citizen. Neither the US nor India can actually help you get in and out of India.
5. Even if you obtain a court order or emergency order preventing them from leaving, the chances of it actually doing so are dismal.
What I would suggest, to be perfectly honest, is that you stay nicey-nice with Mom and get the US passports NOW. Then, you make damn sure that the only parent with possession of the passport is you. Ordinarily I'd suggest that you let the courts "hold" the passports but I fear that's only going to encourage Mom to try the other route - the Indian passport.
This is a horrible, horrible situation and India is not going to give you any help. Would you humor me though please? I'd like to look further than my usual sources to see if there's anything available to help you prevent your children from being removed. I don't feel we're all done here yet.