1

Hi Cielito848!

Welcome to TT!

the train only leaves 1x per day and is earlier than I would like to leave since the wedding will go into the wee hours of the night,

I don't know what train are you talking about. There aren't direct trains from Tarbes to San Sebastián. You have to take a train from Tarbes to Hendaye and an Euskotren train from Hendaye to San Sebastián (aka Donostia). Euskotren trains depart from a tiny train station in the parking of the main SNCF train station.
It seems there are two trains running from Tarbes to Hendaye on Sundays (although we would need to know your specific travel dates to confirm they run on them). Both trains allow you to connect with an Euskotren train to San Sebastián.

2

Trains Tarbes - Bayona - Hendaya on Sundays:
Tarbes dp 8.10 via Dax; 12.04 direct; 14.04 change at Bayonne; 16.16 via Dax; 18.04 direct; 19.26 change at Pau and Bayona, Hendaya ar 23.04; 20.32 change at Bayona, Hendaya ar 23.19
http://telechargement.ter-sncf.com/Images/Aquitaine/Tridion/65-TARBES-PAU-BAYONNE-V2_tcm-11-14684.pdf
http://telechargement.ter-sncf.com/Images/Aquitaine/Tridion/64-BORDEAUX-DAX-PAU-TARBES-V4_2012._tcm-11-14697.pdf
http://telechargement.ter-sncf.com/Images/Aquitaine/Tridion/61-BORDEAUX-DAX-BAYONNE-HENDAYE_V4_14_09_2012_tcm-11-26070.pdf
Due to works along the line, some trains don't run during the whole timetable period (until December 8th).

3

Trains Tarbes - Bayona - Hendaya on Sundays:
Tarbes dp 8.10 via Dax; 12.04 direct; 14.04 change at Bayonne; 16.16 via Dax; 18.04 direct; 19.26 change at Pau and Bayona, Hendaya ar 23.04; 20.32 change at Bayona, Hendaya ar 23.19

I think I should make a nuance to my post in #1. When I said It seems there are two trains running from Tarbes to Hendaye on Sundays, I was talking about direct trains; which would mean less hassle for the OP (Cielito848).
If the OP is fine with options changing trains, neckervd has quoted in #2 options changing trains although, as well as with the direct trains, we would need to know OP's specific travel Sunday to know it they'll run on it.
Be aware the last Euskotren train from Hendaye to San Sebastián departs at 22:33.