Well, first of all Uxmal is not on the way from Merida to PDC. Secondly, all pyramid sites are open over the weekends (except for Xmas .. and perhaps a few other major holidays).
I've never done the drive you mention, but looking at the map I'd decide to drive back from Uxmal to the Periférico of Mérida and then take that east until the Cancun exit. Once you get to Valladolid take the 109 to Tulum and then turn north to PDC.
Merida to Uxmal return would be minimum 2.5 hours; Mérida to PDC another 4. So when you add on another 2-3 hours at Uxmal, you have a long day.
You might want to consider going to Uxmal during your stay in Mérida as a day trip. There are other attractions on the Ruta Puuc that you could add to make a great day out, including a meal at the Pickled Onion.
All ruins in Mexico under the control of The National Institute of Anthropology and History (INAH) sets hours of operation of ruins, they are open 365 days a year from 8AM to 5 PM..........
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