I traveled to and through Mumbai 2 or 3 time as year for 7 years and may have information that could help somewhat.
I usually arrived from Europe on a late night flight and got a room at the LaLit (sp?) that was close to the terminals (1 or 2 km) and had a limo to pick guests up. I found it very convenient to get off the plane and go to my room quickly. I did not pay for the limo because I was a returning guest ,but I suspect it was reasonable. I usually did not check luggage, but the driver was right at the gate and could possibly get the luggage also. - No fighting off the taxi drivers that want to grab your luggage and I like to get to hotel early and not get dropped into a place like Mumbai.
Regarding lounge areas, I always went to the KLM lounge (required company paid KLM membership for business purposes and easy traveling/meeting) in the International terminal rather than wander around the terminal for hours. At that time, some people bought a one day admission. This may be a possibility for you and your husband. Some airlines that have lounges may offer access if you ask them in advance of your flight. I learned to make your way easy and convenient so you can work easily and enjoy the site seeing.
If you are staying at hotel that has a guest lounge try to get into it. It is a good place to meet other travelers. Some ex-pates living nearby even get annual memberships to meet others and talk to travelers. You learn a lot from them.
Enjoy your trip (I always did). Bangalore, Mysore and Agra (if you can get a good hotel there).