"Where is dad?"
Отец = father (very official word). Папа = dad. Папочка [PA-poch-ka], папуля [pa-PU-lya], папаня [pa-PA-nya] = daddy.
The word отец is used pretty rarely. Usually we call our dads "папа". "Отец" is used by the lawyers, in official documents, and in cases when your father is too authoritarian / too far from your soul to be your friend. Just like Luke and Anakin Skywalker in Star Wars ;)
P.S. There is the same situation with мать=mother, мама=mom and мамочка=mommy.
Are you sure it would be used in this context? I believe «пап» is an emerging Vocative form, and it won't be used in this context since here «папа» is not a direct address. Also, it's rarely used in writing.