We are the parents of the 35 wk old twins Lowe2 spoke of and the whole process from their birth on March 11 in Anand to actually getting back to New York City, US on April 17 was a little over 5 weeks. We arrived early in Anand on March 3 just in case. The twins were in NICU for 2 days and we had to wait 10 days for their birth certificates to be issued. During those 10 days we made calls to US Embassy for appointment, then I went online and booked Sofitel Mumbai hotel. I only booked hotel after I got the birth certificate and Medical File. Sofitel was also within walking distance 5 minutes. You will need to have 2 adults to travel by plane. We also consulted with Pediatrician for travel. If you cannot be in India that long and you can have another adult travel to Mumbai with twins then, the most important day(s) that the Father needs to be present is when you are at the Embassy for paperwork. As per Lowe2 suggestion, we booked the Sofitel hotel car pick up from airport. That was great, although much more than regular taxi because we were tired from traveling since 3am. We really did not walk around with twins while in Mumbai, it was too hot for them to be out too long. We did go to the Phoenix shopping center via taxi infront of hotel and bought stuff there. We left the same day after the DNA testing. We had to wait a week after that for the DNA test kit to travel back to US and results. We did pay for the expedited processing for DNA test. After the results were sent to US Embassy and it took a few days for verification and printing of passports. We requested the passport copies be scanned and emailed so we could start the Indian Exit Visa process while waiting for actual passports in the mail. I did end up going directly to Courier office to pick Passports since they had arrived in Anand but by day 2 of waiting for delivery at Rama, because I was getting impatient. You will need to show proof of children's airplane ticket travel for Exit Visa.
I hope this information helps you and others getting ready.