I think the OP's question is being unnecessarily complicated.

Some points:

* X5 is expensive in India - the luxury car makers each sell fewer than 1000 cars a year in a country of a billion people. This is not the place to demand a German luxury marque.

* As mentioned the Toyota Innova is extremely readily available and is a large car produced around Asia and costs around one third more than the basic undersized Indian Tata Indica. The Innova enjoys higher ride height than standard sedan models and is well worth the extra money not to mention having space for up to eight (including driver).

* Although I didn't take it, I was very firmly advised to allow MINIMUM 4.5 hours but typically 5+ for the Delhi-Agra trip. By contrast the Shabatdi Express does the trip in 2 hours, and other lesser trains in 3 hours. While the trains are not 100% luxurious, it is still a more comfortable option than a BMW X5. I saw some very fat people on the train, which although normally overbooked tends in fact to have seats to spare - on the Shabadti Express the standard AC Chair Class is quite ok but the First Class has more space.

* We found our various Innovas in India quite ok, but would very strongly recommend http://www.travelbureauagra.com/ We paid something around $50 for an Innova with a driver who spoke VERY good English (a graduate) at our disposal from 11am till 7pm in Agra. The driver was entirely on a par with those we had from the Oberoi (who charged 3x more). In addition, we had a very tight connection in Delhi from our train, which allegedly arrives at 10:30pm, and our plane at 1:30am, stopping via the Oberoi New Delhi to pick up bags. The owner of Agra Travel Bureau made a booking for us in Delhi, which cost again $50 for this trip and these guys were very good - two staff waiting on the platform at the train station (the Oberoi drivers refused to enter) and then a proper sense of urgency speeding through Delhi to the airport before walking us to the check-in counter (the train of course was one hour late, as I think is fairly common in India) in person to deal with the staff and ensure we got on the train.

So, forget the X5 entirely, have a look at train times on www.cleartrip.com, you need to avoid 'Second Sitting' and 'Sleeper Class' but the others are ok, and then just get the driver for the Agra area.

The hotel suggestion for Agra of Amarvilas is ok and the view is very fine indeed, however the hotel itself is rather impersonal and lacklustre compared with other Oberois due to the endless procession of daytripping Taj Mahal visitors. Certainly a far better use of your money than spending 10 hours+ in an overpriced BMW however.