Did divorce occur when the wife returned from her family's home, bringing with her a gift from a neighbor, knowing that the husband had sworn that divorce would occur if she brought anything from her family's home, and does the oath remain valid thereafter?

The reference for an oath is the intention of the one swearing it and what he meant by his oath. If you intended specifically your wife's family or a particular purpose, and did not intend trivial matters or things concerning children, then no breach of oath (hith) or divorce (talaq) occurs. However, if you intended a general prohibition, and something falling under it occurred, then the breach of oath and divorce have occurred.

If the divorce occurred and it was not the third (irrevocable) one, you can take your wife back (raj'a) as long as she is within her waiting period (iddah) by saying: "I have taken you back to my wedlock." However, if the waiting period has ended, then a new marriage contract is necessary.

This oath is dissolved by its breach the first time and is not repeated unless you intended to repeat the breach or the wording of the oath implied repetition with words like "every time." One must be careful about marital problems and keen to resolve them wisely, avoiding divorce.