Is what the husband did, going to Rotterdam after saying he was going for a walk, considered a lie, and is the sister entitled to ask for forgiveness from her in-laws despite her feeling of injustice?

It is not the sister's right to prevent her husband from going to his parents' house or anywhere else, nor is the husband obliged to inform his wife of his destination. He may use allusion (ta'ridh) and equivocation (tawriyah) if he deems it beneficial to conceal the information.

The husband's parents are not obliged to inform their son's wife of his visit to them.

The issue does not warrant discord. If the husband curses his wife, he is mistaken.

The sister is advised to cease discord and to live together in kindness, and to seek forgiveness from her husband's parents.