All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Scholars have stated that obedience to parents is an obligation if there is a benefit for the parents while there is no hardship on the children.
If the parents of this young man had a valid reason for him not to go to that distant mosque, such as fearing actual harm on him and not just due to unrealistic fear, then he must obey them. But, if they did not have a valid reason, but merely because of intolerance due to ignorance and the like, or he may be harmed in his religious or worldly affairs by praying in the nearby mosque, for example, then in this case he is not obliged to obey them.
However, we advise him to be polite and kind with them and endeavor to convince them and seek the help of whoever might influence them, in addition to asking the help of Allah the Exalted and supplicating Him.
We point out that the fact that the mosque follows the Hanafi school of Jurisprudence does not contradict the fact that it is in accordance with the belief of Ahl as-Sunnah wal-Jama’ah, and in case of a disagreement between the reputable Schools of Jurisprudence (madhaa'hib) in a particular part, it falls upon the person if he knows the most preponderant view to act according to it.
Allah knows best.