No difference between them in meaning. Сердце моё is more literary than моё сердце. The author wrote this sentence in this way just to make it more impressive. Take a look at this example: Моя любовь- любовь моя Both have the same meaning but the second option is more romantic and impressive than the first option. So if you want to call your girlfriend or wife, call her "любовь моя"! That impresses her more!

"моё cердце" - может быть просто констатация принадлежности сердца "cердце моё" - придание ритма в изложении мысли "cердце моё" - как обращение к любимой или к ребёнку

Actually, there is no difference in meaning, but the order of words can be changed for the rythm in songs.

And what the difference between "Heart of a mother" and "Mother's heart"? We emphasize the last word in these phrase.

There is no difference between these two sentences. Because there are six cases in Russian language so you can put the words in any order and it makes sense. But as Farid said sometimes it can be more literary or more conversational.