Is it permissible for a mother to prevent her married son from traveling for leisure with his wife and children unless she accompanies them, and would he be sinful if he sometimes traveled without her, knowing that her presence restricts intimacy between the couple? And is it permissible to lie to her or not inform her?

The mother does not have the right to prevent her son from traveling with his wife and children as long as he provides her with what she needs. There is no sin upon the son for traveling without her, but it is better to obey her if it does not harm him or his family. A righteous wife should help her husband in honoring his mother. There is no harm for the husband in traveling with his wife and children without informing his mother, and he can use allusive statements (ma'arid) if he needs to lie.