Their mother's language would be השפה של אמא I believe, but that's a different thing from "mother tongue". Usually, one would share a mother tongue with one's parents, but not necessarily. שפת אם is specific to one's mother or native tongue, it doesn't (necessarily) mean the language one's mother speaks.
What's the question? A mother's language is the language of the mother. A mother tongue is a native language. Example: my mother's languages are Yiddish and English. My mother tongue is English. (Personally I think tongue sounds weird, and instead just say native language: my native language is American English).