And peace be upon you, and the mercy and blessings of Allah.
Grand Ayatollah Sayyid Khamenei and Grand Ayatollah Sayyid Sistani (may Allah protect them):
Yes. It is obligatory upon fathers and mothers to guide and direct their children who have reached the age of religious responsibility (Taklif) and must choose a Marja to emulate, as the difficulty of understanding the issue of emulation may prevent them from identifying their religious duty on their own.
However, if the children later reach a conviction that another scholar is more learned (al-A’lam), or that the parents' method of guidance was incorrect, they must then investigate and emulate the most learned. To learn the method of identifying the most learned and the manner of emulation, you may refer to Question 568.
May you remain successful in all that is good.
Sources
Grand Ayatollah Sayyid Khamenei: The Educational Treatise — Emulation — Emulation (2) — Some notes regarding the conditions of a Marja of emulation.
Grand Ayatollah Sayyid Sistani: Jurisprudence Made Easy — Dialogue on Emulation — Why do we emulate?