Sanskrit is not the mother of all languages. Sanskrit is not even the mother of the modern Indo-Aryan languages of the Northern India. Neither it is their father or grandfather. In fact, no language is a direct descendant of Sanskrit.
Saying that Sanskrit to the modern Indo-Aryan languages is the same as Latin to the modern Romance languages is absolutely wrong. The Romance languages are direct descendants of Latin, but the modern Indo-Aryan languages are not direct descendants of Sanskrit. The best European analogy is the role Ancient Greek played for the modern European languages: Ancient Greek affected them all, filled them with lots of words and syntactic structures, but none of those languages is a direct descendant of Ancient Greek, naturally with the exception of modern Greek.
If toTo continue the family analogy, to the modern Indo-Aryan languages Sanskrit is a cousin grandfather who was their teacher, their guru. The Indo-Aryan languages descend from grandfather's siblings, but grandfather himself had no children.
Speaking more linguistically, there are actually two languages called Sanskrit: the Vedic Sanskrit aka the Vedic language (ca. 1500 to 500 BCE), and Sanskrit proper aka Classical Sanskrit (ca. 200 CE to 1300 CE), the latter being a refined and artistic, highly elaborate version of the former. The Vedic language was once a vernacular, but since the texts in it were holy and highly revered, the language was later standardized and it underwent polishing by Indian sages and philosophers giving rise to Sanskrit whose name can be translated as "well prepared, pure and perfect, polished". But apart from Sanskrit proper, the Vedic language gave rise to its sister languages, not so refined, not so polished, but which were really vernacular languages in the times when Sanskrit bekamebecame the language of educated philosophers, brahmanasbrahmins, and poets. Those sister languages are called Prakrits, "natural, original, unpolished", the main ones being Maharashtri, Gandhari, Shauraseni, and Magadhi. Pali can also be considered a Prakrit, although later they did polish it very much. The Prakrits are the Middle Indo-Aryan languages, it is from them that the Modern Indo-Aryan languages developed.