one of my wife's relatives'

English as a Second Language English Vocabulary, Grammar and Idioms
1
  1. I had dinner at one of my wife’s relative’s (house) yesterday.
  2. I had dinner at one of my wife’s relatives’ (house) yesterday.
    Which one is correct?
    Thanks.
2

As you are using ‘one of’ then the singular
relative’s
is correct.
Do not include the word ‘house’ in that particular sentence. I suspect you only put it there to explain what you meant. You would need to say
I had dinner at one of my wife’s relative’s houses… which is really ambiguous and makes it sound as if there are a number of houses.

It would be better to say:
I had dinner at my wife’s relative’s house last night. (singular relative)
I had dinner at my wife’s relatives’ house last night. (plural relative)
or, if location is not important, even more simply:
I had dinner with my wife’s relative(s) last night.

3

Beeesneees,
“I had dinner at one of my brothers’ yesterday.”
Is this sentence correct?
Thanks.

4

It’s passable but once again it would be more clear if you said:
I had dinner at my brother’s house.
even though you may have other brothers.