Annie, my information is that there are no direct train links from Santiago de Compostela to Porto and one has to go via Vigo.
http://www.renfe.es/ or the Spanish train timetables.
http://www.cp.pt for the Portuguese train timetables.
There are two trains daily between Vigo and Porto. Connecting Services as follows:
Santiago da Compostela: 05:50 Vigo: 07:37 Vigo: 07:40 Porto: 09:55
Santago da Compostela: 17:38 Vigo: 18:59 Vigo: 19:44 Porto: 21:55
The bus from Santiago goes straight to Porto and the airport, twice a day, for 22 euros, and then
on to Fatima, Lisboa.
http://www.alsa.es for the bus timetables.
By Bus: Santiago to Porto – Fatima – Lisbon
http://www.alsa.es
2.45hrs costs 22euro one way 10am 17pm 10pm 22pm
If you take a train to Vigo there is a direct bus service to Oporto airport and city.
http://www.autna.com/regulares.php for the bus service schedule click on servicios
As you will be travelling on a Sunday, other things to note are; Sunday and Public holiday services are usually reduced, when compared with the rest of the week so check the timetables. There is an hours’ difference between the two countries.