What is the Sharia ruling on a divorce that was issued by the husband twice, once at the beginning of the marriage and again after 6 or 7 months, then the couple returned to their normal life? And is the wife's continued presence with her husband in this situation considered adultery?

Casting the oath of divorce (talaq) is either immediate, in which case one divorce occurs, or conditional, in which case the divorce does not occur unless the condition upon which the divorce was suspended takes place.

If the divorce occurs, whether immediate or conditional, and the condition upon which it was suspended takes place, and you have been divorced twice, then the man may take back his wife during her 'iddah (waiting period) without a new contract or mahr (dower), or after her 'iddah ends with a new contract and mahr.

However, if the oath of divorce was conditional and the condition upon which the divorce was suspended did not occur, then no divorce takes place, and the man still has three divorces remaining with his wife.

The summary is that you are his wife in both scenarios.