Is it grammatically correct to shift an appositive away from the noun it renames or describes?

I'm taking a semester in London. Here's a sample of something I keep hearing:

John: My mum will be here later?

Susan: Is she staying for supper, your mum?

If Susan wishes to say, "your mum," why can't she just ask:

Is your mum staying for dinner?

Or, if Susan wants to clarify who that she in her sentence is (for which, in my opinion, there is absolutely no need), why doesn't she just say:

"Is she, your mum, staying for dinner?"

Is there anything in grammar that allows for putting an appositive not immediately next to what it's describing?

If so, how is it justified?

Regard the following sentence:

• Bob's a mighty fine guy.

The Subject of this sentence, clearly, is Bob. Now consider this one:

• Bob, he's a mighty fine guy.

Here Bob has been shunted to the left of the clause. The word Bob is now like an announcement of the topic of the rest of the sentence. This is known as a left dislocation. Some constituent of the sentence has been dislocated to the left of the nucleus of the clause and then a co-referential pronoun, he, has been used to plug that gap. The grammatical Subject of this clause is now the word he.

Left disclocated elements do not always represent Subjects. Consider the following joke:

• Men, you can't live with them and you can't kill them.

Here men is coreferential with the object of the preposition with. Again, it announces the topic of the sentence.

We can also have right dislocations too:

• He's a mighty fine guy, Bob.

Here the Subject has been dislocated to the right of the clause. Right disclocations tend to affirm the identity of some co-referential element in the sentence, in this case the pronoun he.

The Original Poster's Question

Is she staying for supper, your mum?

This is a perfectly grammatical sentence. It is an example of a right dislocation. Perfectly grammatical though it is, we only tend to see this sort of construction in spoken English or quite informal writing.

Yes, it's grammatically correct. It's an issue of syntax within grammar. It's called dislocation.

In syntax, dislocation is a sentence structure in which a constituent which could otherwise be either an argument or an adjunct of the clause occurs outside the clause boundaries either to its left or to its right as in English:

Your mum, is she staying for dinner?

Is she staying for dinner, your mum?

These two sentences say the same thing. The only difference is the direction of dislocation.

The dislocated element is often separated by a pause, a comma in writing, from a clause. Its place within the clause is often occupied by a pronoun like she does in your example.

There are two types of dislocation: right dislocation, in which the constituent is postponed as in your example, and left dislocation, in which it is advanced. Right dislocation often occurs with a clarifying afterthought, e.g., Is she coming to dinner. "Your mum" is added afterward to clarify exactly who they are.