Would we be able to book a car for the two days that we are in Delhi?
Yes. If you inform the hotel management, they make arrangements. They are quite reasonable. I availed a car service from them. It was for one day Delhi sight seeing tour. There are two options available - 4 hours and 40 kms it is Rs.800/-. If you have it for 8 hours and 80 kms, it will be Rs. 1500/-. I have avilaed it for 8 hours. Thier airport drop charge is Rs.600/-. Apart from this, there are also radio taxi available in Delhi like Meru cabs, etc.
Get an answer from Hotel Intercity staff and past guests.