"to each other..."? What's the best way to say it?

[Tack]

Hi,
would appreciate a little help please
I'm in the middle of a composition that I am writing.
I want to write

"They said 'good night' to each other".

Or at least express the concept.
So far - best I can do is :-

お互いに「お休みなさい」と言いました.

I have left the subjects out (They) as it can be inferred from the rest of the composition.....

However, I have had a bit of trouble finding examples to compare with or details on this sort of construction.
1) Not sure the "お" is necessary as it appears to be an honorific　and contextually <?> not required??
2) Not sure if the use of お互いに is correct in position in the sentence - or indeed - at all!
3) Lastly - if I was NOT directly quoting speech, is there a set expression used to describe a parting of friends in this situation.

Thanks for any suggestions!

[WalterWills]

My Japanese isn't great so I'm not sure but...

1. I don't think the prefix is necessary, because it relates to the people in the story, and not to anyone who would read it, so nobody could be offended by its omission.

2. I think it's correct. I would write:

互いに「お休みなさい」と言いました。
Or:
「お休みなさい」と互いに言いました。

I looked in my dictionary and an example it has is:
彼らは互いに憎み合っている
(They hate eachother)

3. I don't know.