"My wife's father has dark hair."
Translation:У отца моей жены тёмные волосы.
Тесть = father-in-law, отец жены = wife's father.
Я с вами согласен, но.... редко какой мужчина в России скажет "отец жены".
А уж про father-in-law без контекста и вовсе не разберёшься, то ли "тесть", то ли "свёкор".
Я согласен, что «тесть» тоже должно приниматься.
It is close to Dad and Father. Papa is usually only used with ones own Dad or speaking about a child's Dad. If it is your wife's father - отец sounds a lot better.
«У отца́» is more formal than «у па́пы». It's similar to the English words 'father' and 'Dad' (although I can't vouch the usage is completely the same).
In this sentence the first genitive is part of the Y+GEN expression and the second is simple possession. The idea of "having" is encapsulated in "у + gen" so if you start with "моей жены" first then she is the one who will have dark hair, not her father. The correct answer means "The father of my wife has...." Switching it as you write would mean. "My wife of father"... it doesn't really make sense.