I'm in the process of planning our first journey to India for late Dec-early Jan 2013 to celebrate our 10 year wedding anniversary. I'm very happy with the itinerary for the first half of our stay, bar the question of whether or not Aman New Delhi is the best choice for us. I love Aman resorts and Aman New Delhi gets some great reviews but I wondered if there was anywhere else that we should consider? We will be dining at the hotel we stay at and I'm curious if there's another hotel on par with Aman that might have more authentic Indian dining options or if the Indian food at Aman New Delhi is as good as any major hotel. So here's the itinerary so far - I've highlighted my questions in red.

2 nights Aman New Delhi - is there another hotel we should consider?
Transfer by train to Agra
2 nights Oberoi Amar Villas
car transfer from Agra to Amanbagh
3 nights Amanbagh

It's after this that I need some help. We want to got to either Taj Umaid Bhawan Palace in Jodhpur for 3 nights or to Oberoi Udaivilas in Udaipur for 3 nights. Which one would you recommend and why? They both look stunning but I'd be interested to know if the local excursions and nearby sites are better at one than the other. From what I can tell we would need to get to both by transferring from Amanbagh by car to Jaipur airport and then taking a flight. Is that he best way?

Once that choice has been made I would then like to go to Aman-i-Khas for 3 nights - what's the best way to transfer from either of the above to Aman-i-Khas?
After Aman-i-Khas we would then like to return to Delhi for 2 nights before returning home. Would you recommend transferring between aman-i-Khas to Delhi by train or flying?
Two final questions, firstly is it warm enough in late December/ early Jan to be able to swim and enjoy the pools at these properties? And can anyone recommend a good Virtuoso agent that we can use to book the trip for us.

A lot of questions but any advice you have or suggestions you can make that you think will enhance our trip will be greatly appreciated.