Is the phrase "we live together, raise children, and do not sleep together," intended to mean abstaining from sexual intercourse while jointly raising children, considered an implicit divorce (kinayah fi al-talaq) by which divorce takes effect with the intention, or is it not an implicit divorce at all? And does what the questioner mentioned about his intention with this phrase result in divorce?

Praise be to Allah that you have come to know that the intrusive thoughts about divorce are not a divorce but rather a whisper (waswasa). The Sheikh's fatwa applies to one who is certain of the occurrence of divorce but doubts its number, not to one who doubts the occurrence of divorce itself. Therefore, nothing is binding upon someone in your situation. And your statement: "We live together, raise the children, but do not sleep together" does not necessitate a divorce, because you did not intend to initiate a divorce by it. Rather, you sought a solution to the problem, and this is due to the obsessive-compulsive whispers you suffer from. The one afflicted by waswasa regarding divorce is not like others.