Are the two divorces that occurred—the first over the phone, and the second a month and a half later, knowing that the husband did not take his wife back after the first divorce—counted as two divorces or one divorce?

The majority of scholars hold that successive divorces all take effect, whether a revocable return (rajʿah) intervenes or not. This is the fatwa given. Based on this, you have pronounced two divorces upon your wife. As long as the divorce is less than three, you may take her back during her waiting period (ʿiddah) without the need for a new marriage contract.