If a husband says to his wife over the phone: "If I find out that you were the one who told my mother, then you are no longer my responsibility," and he later discovers that she was indeed the one who told his mother, does a single divorce count occur?

Your statement to your wife: "If I discover that you are the one who told my mother, then you are not under my responsibility (not my wife)" is one of the allusions to divorce. Its effect depends on your intention. If you intended divorce, then one divorce takes place if it becomes clear that she was the one who told your mother. You can take her back (perform raj'a) as long as she is within her waiting period (iddah (definition)), provided you have consummated the marriage and this was the first or second divorce. However, if you have not consummated the marriage, it is considered a minor irrevocable divorce (baynunah sughra), and she is not lawful for you except with a new marriage contract. If you did not intend divorce with your words, then nothing takes place.