a two-week's holiday / a two-week holiday

[demir]

Could you kindly explain which of the following uses is true?

I have just returned from a two-week holiday (or, a two- week trip) / a two-week's holiday (or, a two-week's trip.

Thanks in advance.

[Anglika]

A two-week holiday
OR
Two weeks' holiday

I have just returned from a two-week holiday.

I have just returned after two weeks' holiday.

[demir]

A two-week holiday
OR
Two weeks' holiday

I have just returned from a two-week holiday.

I have just returned after two weeks' holiday.

Thank you for your quick reply, Anglika.

I would like to ask one more thing:

If we could say ' a week's holiday' why not ' a two-week's holiday'

[MisterJack]

"two-week" written with an hyphen ("-") functions as an adjective. You can never add " 's" to an English adjective.
On the other hand, "two weeks" indicates a duration with an numeral adjective and a noun. In that case you can use the saxon genitive to indicate a period of time.