Regard the following sentence:
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.