There may not be anything wrong with the language, but with the family :) I wonder who might ask for permission to "come home for Christmas", only to be told (by his father ??) that
that person's wife will decide. Does anybody agree there is some incongruity between the intimacy of the situation and
the wording of this sentence ?

it could be a lone guy who is desperate to spend Christmas at some friend's...

In that case I would expect the reported question to be:
If you may come to my home / come home with me ...
The original sentence implies that that place still is, or at least used to be, the other person's home,too.

Well, I don't wish to kill off the Christmas spirit, so ok, let it ride. :)

that is why I put a tag "@Needs Native Check". I precisely want to verify this. My instinct, in that case, is that "home" implicitly refers to the speaker's home, in the context. I might be wrong.
Let's see what natives say...

But another context could be: The person the speaker is speaking to is his/her child who has stranded somewhere and begs to come back home for Christmas, and the speaker, who has remarried in between, wants to ask his/her (they could be lesbians) new partner...
In that case, "home" would be everybody's...although one has to ask permission...

CK, we are all in agreement on the general meaning, the problem with this sentence is, how realistic is it in the given situation? Sacredceltic's interpretation is possible, I suppose.
What I was getting at is: Somebody who asks for permission to "come home" for Christmas is referring to what is , or used to be, his own home. The person he asks is very likely to be a close relative, probably his/her father. Even if there is so much tension in the family that the father answers ironically, he will say "I'll ask your mother" rather than "I'll ask my wife". And if he had remarried, he would say "I'll ask your stepmother".
If, on the other hand, somebody outside the family asked for permission to spend Christmas with the speaker, he wouldn't ask if he or she could "come home" -I think.

@PeterR

I think there is a misunderstanding here. It is NOT a dialogue (I inserted no quoting marks). It is the same speaker all along, in what we can suppose is a phone call.
The first leg of the sentence is a rewording, by this unique speaker, of what we may suppose was a request (that is NOT there), by his/her interlocutor to spend Christmas at "home".
In intepretation 1, "home" is implicitly the home of the speaker. (then the interlocutor might be a lone friend)
In interpretation 2, "home" could be the home of both (then the interlocutor might be an estranged child)

so CK's interpretation is broadly correct:
"I don't know if you can come to our house for Christmas or not. I'll ask my wife and let you know."

The French doesn't explicitly say "ask" but "toucher deux mots" which means to "mention" because we can suppose it is a delicate matter that the person doesn't want to directly request...

>Even if there is so much tension in the family that the father answers ironically, he will say "I'll ask your mother" rather than "I'll ask my wife". And if he had remarried, he would say "I'll ask your stepmother".

I disagree.
In the case this is a child, it might perfectly be that the tension with the "stepmother" is such that the child refuses to call her so, and the husband/wife would refer to her as "my wife".
I actually know circumstances where this is the case.
Besides, in French, it's not usual that people refer ironically to their partner as "my wife/my husband" even when talking to their kids...

>If the speaker says just "home", then it is implied that the listener and speaker are from the same home. It would be "my house" if he's talking to a friend.

agreed.

>The end should be, "... and I'll tell you what she says."

Do you mean to say that "I'll tell you what" is not correct? I heard and read this more than once...

thank you for your pain, Nero. I corrected the "what".

As I explained earlier, the child scenario might sound a bit far-fetched but it's not impossible. I know people who've been married 4 or 5 times and just say "my wife" because they don't risk mixing up names which is guaranteed to create havoc and ruin Christmas...

Another scenario I can picture is the guy is speaking to his brother or sister, and they live in their childhood house that he inherited from his parents, so he would still refer to their former common house as "home"...

>While these scenarios are plausible, it seems to burden the sentence with having strict qualifications.

Isn't that the case with ALL sentences?
Learning a language doesn't consist in learning mere words, but learning their qualifications, which differ from language to language, culture to culture.
It's interesting to see, for instance, that the simplest sentences are the most difficult to translate, because their qualifications never match what the words would have us believe they meant in the first place.
I constantly insert sentences with strict qualifications in the Corpus...