Hi CarlyA! Welcome to the forum!
León-San Martín del Camino; San Martín del Camino-Astorga are made by Alsa:
www.alsa.es/en
From Astorga to Foncebadón, Autocares Pedrín (
http://autocarespedrin.e.telefonica.net) has buses but I think they don't run daily so check with them once on the ground. From Foncebadón to Ponferrada, AFAIK, there aren't buses. I would suggest to go all the way from Astorga to Ponferrada (either by bus or train) even if that means your dad and daughter miss you one night.
Astorga-Ponferrada; Ponferrada-Villafranca del Bierzo; Villafranca del Bierzo-Pedrafita do Cebreiro (roughly 4 kms away from O Cebreiro) are made by Alsa. Once in Pedrafita do Cebreiro, you can take a taxi to O Cebreiro because the bus from Pedrafita do Cebreiro to O Cebreiro departs early in the morning.
Pedrafita do Cebreiro-O Cebreiro; O Cebreiro-Triacastela and Triacastela-Sarria are made by Monbus:
www.monbus.es There isn't service on Sundays.
Sarria-Portomarín is made by Empresa Portomarín:
www.empresaportomarin.com
From Portomarín to Palas de Rei there aren't direct buses. For that strecht you have two options to take a taxi (quicker) or to make the route changing buses in Lugo (a big detour but probably -way- cheaper). The bus companies making the route from Portomarín to Lugo are Empresa Portomarín (this one makes it daily and offers more frequencies) and Monbus. From Lugo to Palas de Rei, the bus company that makes it is Empresa Freire.
Palas de Rei-Arzúa; Arzúa-O Pedrouzo and O Pedrouzo-Santiago de Compostela are made by Empresa Freire:
www.empresafreire.com