We just did a day trip to taj and Agra fort from Delhi using the Yamuna expressway. Left Hyatt Delhi at 7 and were inside taj complex at 10. Left Agra fort at 2.15 and were at Hyatt at 4.45. It was longer in the am as commercial vehicles registered in Delhi have to pay a tax in UP that's a little out of the way in noida. We used Hyatt Delhi concierge and paid about 18k including use of a guide at taj mahal and fort . Had lunch at ITC Agra.

Quite doable. Only one Word of caution due to high speeds on the expressway the number of tire bursts have been high. If you do hire any local guy make sure for your safety you moderate his speed. We stayed under 120 all the way and still made good.

Secondly if you buy the 750 rupee foreign ticket it avoids the long lines. Entry for the 20 rupee ticket holders is all way way circular behind taj and painful in the heat. The other benefit is you get shoe covers and water bottle for that. Plus entry into the tomb itself is allowed at a higher rate for the foreign ticket. Finally make sure you save the ticket as it gets one 50 rupees off at the fort entrance.