Hi, I don't know anything about language training. But if she loves your daughter, and takes care of her with her heart, then you are lucky! You can trust her to look after her well when you are away.
I think it is okay to listen or sing songs in whatever language. It is only a game to children and they won't look into the real meaning of these songs. But for daily oral language, it's better to talk more in Cantonese to your kid.