For Nathdwara, you have to get down at Falna station between Abu Road and Ajmer. Falna is 307 kms from Ahmedabad. Many trains like Ranakpur Express/4708 , Bandra Sarai Rohilla Exp/2216, Suryanagri Exp/2480 etc all going via Ahmedabad.
One more train from Mumbai which goes directly to Mavli Jn. from where Nathdwara is just 27 kms. is Udaipur. That is Bandra Udaipur Super Fast Express / 2995 train on Sun/Wed/Fri. It reaches Mavli Jn. at 8.00 am in the morning and before 9.00 am you can reach Nathdwara.