Your poor abandoned original thread is here:  Help: Possible Yorkshire Ballad?  One reason for encouraging people to stick with their original enquiry rather than starting new threads a day or so later is to avoid making life unnecessarily difficult for future enquirers.

That said, and now that work has eased a little and I have time to reply, I suspect that your best chance of getting somewhere with this lies not in the field of traditional music but in those of folktale studies and literary criticism.  You can be fairly sure that some student of the Brontes has at some time adressed this question; probably they have got nowhere with it, but it is an avenue which you should explore if you have not already done so: start with the biggest academic study of Wuthering Heights that you can find, and work through the bibliography.  Small pieces in learned periodicals are often the best source of information about the minutiae of literary works; as time goes on it becomes harder and harder for higher-degree students to find something to write about that hasn't been done to death, and wee questions like this are an absolute godsend for them if there is an answer to be found.

You should also consult Stith Thompson's Motif-Index of Folk-Literature, and Katherine Briggs' Dictionary of British Folk-Tales in the English Language.  I strongly suspect that you will find nothing in the way of a putative ballad on the subject; very probably, there never was one.  What you may very well find is a range of folktales containing this motif (which I take to be something on the lines of dead mother responds to her children's distress), somewhere amongst which might perhaps be a recognisable relative of a story which may have inspired Miss Bronte's little fragment.