Tarragona has two railway stations. Camp Tarragona is served by high speed trains and Tarragona railway station has normal trains. Camp Tarragona is around 15-20 minutes by taxi from Tarragona. Make sure you know which station you want. If you are doing a day trip from Bar elona then Tarragona station is best as it's a 15 minute walk to the historic centre of Tarragona.
We travelled from Barcelona-Sants to Tarragona two weeks ago. I was able to book our tickets in the Renfe app on a Regional Express train 15049 but I was only able to book a seniors fare because my husband has a Tarjeta Dorada (senior discount card). Our train arrived at Tarragona station which is right in town.
You can also catch the Rodalies train line R16 from Passeig de Gracia or Barcelona-Sants to Tarragona. You can't buy these tickets online in advance, you just buy them at the station on the day from either a ticket machine or ticket office. We traveled between Barcelona and Tarragona this way in October 2022 for a day trip.
If you are having difficulty booking a return ticket look for "ida y vuelta" as the ticket option (there and back = return) or just book two single trips, one Barcelona to Tarragona and one Tarragona to Barcelona.
If it's the Renfe app causing the problem try using the Trainline which I used for some of our Spanish train trips and found very easy to use.
