My sense (although it is difficult to judge as everyone has different values/tolerances regarding the intensity of a trip like this) is that your itinerary may be a bit too exhaustive and thus exhausting. I think a good rule of thumb in India is to try for 3-4 nights per location, with the exception of Agra, where 2 is fine. And really, your itinerary does that well -- with 3 nights at Amanbagh, Udaivilas, and Aman-i-Khas. So if you are an energetic traveler with a lot of tolerance for time spent in transit, perhaps this itinerary will work really well for you. But if you're at all worried about not having enough time to spend afternoons by the pool, indulge in spa treatments, etc., you may want to cut one of your destinations and add some nights. If a stay is for 2 nights, you really only have one full day at a site before you're consumed again in transfers, which can be more exhausting in India than anywhere else I've been.
So I'll offer some recommended adjustments to your itinerary below, but please know that I do so in a spirit of total humility, as I really don't know your preferences well enough to offer advice with confidence. In a nutshell, I think you should cut just one of your destinations, and spread those days across the other destinations so as to reduce the amount of transfers you're doing and have time to really soak up the various destinations:
Arrival to New Delhi and transfer to Aman New Delhi - Complimentary car transfer - transfer time approx. 45 minutes
2 nights - Aman New Delhi
GROOMBRIDGE perspective: I would add one night here rather than returning to Aman New Delhi at the end of your trip. Aman New Delhi has some very special bespoke experiences within Delhi that could be a really wonderful way to begin your trip, and you'll also love unwinding by the pool, in the spa, etc.
Car transfer to Agra - drive time 4.5 hours
GROOMBRIDGE perspective: I beg you, if there is only one change you make to this itinerary, please do not go by car from Delhi to Agra. I've done this trip both by car and by the once-daily luxury train (which leaves Delhi around 6 am). Aman New Delhi can arrange that for you, and it is not just much faster, but much less stressful and a much smoother ride. I know others on this board will agree with me -- the drive was one of the only two truly horrible experiences we had in India, the other being the drive from Jodhpur-Udaipur (more on that later . . . ) Aman will acquire your train tickets and deliver you directly onto the luxury train, and Oberoi Amarvilas will meet you in Agra's train station. When I head this advice from others, I couldn't imagine why I was receiving it, but the drive is truly horrific -- constant potholes, stop-and-start traffic, etc., none of which you have to experience on the luxury train, the fastest, safest, and smoothest way to get from Delhi to Agra.
2 nights Agra - Oberoi Amar Villas
GROOMBRIDGE perspective: So glad you're staying 2 nights, so you can enjoy the beautiful pool and facilities while also seeing incredible Mughal ruins like Fatephur Sikri (which you may want to see en route to Amanbagh).
Transfer from Agra to Amanbagh - approximate drive time 4.5 hours
GROOMBRIDGE: This drive is the only drive I can wholeheartedly recommend within your itinerary. Smooth, high quality roads with limited traffic issues. Aman will do this for you very well. 4.5 hours is a worst-case scenario -- we did it in closer to 2.5.
3 nights - Amanbagh
GROOMBRIDGE:
I'd perhaps add a 4th night at Amanbagh, as there are so many bespoke local excursions and experiences, and this is India at its most authentic and untouristed, with such warm and friendly villagers. With the rapid urbanization of India, Amanbagh opens up an Indian experience that is rapidly disappearing.
Car transfer to Jaipur and flight to Jodhpur – Transfer time to Jaipur approx 2 hours and flight time approx. 1 h 20 min to Jodhpur
GROOMBRIDGE: Perfect. This is the exact same transfer we did, and it worked very well.
2 nights – Jodhpur Bhawan Palace
GROOMBRIDGE: I'd also perhaps add a 3rd night here, to give you time really to soak up the experience of living in that palace. I didn't feel there was a huge amount to see in Jodhpur itself, but you really might want two full days to see the few sites AND to spend time relaxing at the pool and indulging in the splendor that is Umaid Bhawan.
Drive to Udaipur - 5 Hours
GROOMBRIDGE: Is there not a flight available? The good thing about the drive is that you can stop at the spectacular Jain temples at about the halfway mark. But the drive is excruciating, like the one from Delhi to Agra, with constant start-and-stop traffic. If at all possible to fly, that would be better.
3 nights -Udaipur Udaivilas (Own arrangement)
GROOMBRIDGE: I think that's the perfect number of nights in Udaipur. But by adding 1 night to Aman New Delhi, Amanbagh, and Umaid Bhawan Palace, you may now want to fly from Udaipur to Delhi airport, and rather than dealing with the hassle of transfers to/from the airport, arrange to fly home from Delhi from there.
Flight transfer from Udaipur to Jaipur - and transfer to Aman-I-Khas - drive time from Jaipur to Aman-I-Khas - approx. 3 hours
GROOMBRIDGE: No one could have talked me out of Aman-i-Khas, given positive feedback about it on this board and my trust in Aman. But the tiger sitings are rare and difficult at the time of year you're going, and the hassle of getting to and from Aman-i-Khas was not worth it to me, and may not be for you. If I were doing your trip, having experienced these same places, I would cut Aman-i-Khas.
3 nights - Aman-I-Khas
Train transfer to New Delhi and transfer to Aman New Delhi
GROOMBRIDGE: This train transfer is rough, as it is NOT a luxury train, so is quite primitive and is a long journey. There's not really another option . . . which may argue from striking Aman-i-Khas from your itinerary.
1 night - Aman New Delhi - Overnight at Aman New Delhi - rest and unwind before your international departure