"We need the names of their mothers and fathers."
Translation:Potřebujeme jména jejich matek a otců.
Two reasons. The course sticks to formal "mother= matka" and "father = otec". You can get mom and dat and in such a case we go for máma a táta. The system does not have diminutives at the moment.
The second one is, even if we did accept 'tatínek:, nobody would ever mix it with "matka". Once you use diminutive for one, you use the same for the other, because it just simply sounds funny.
Potřebujeme jména jejich maminek a tatínků....