Is the phrase "You will not leave, and if you leave, you are no longer under my responsibility" considered a divorce, if the intention was for her not to go to a specific supermarket and the wife did not go there, and does this entail a prohibition for her to go to that supermarket or to leave the house at all, or is the ruling nullified after the day passes?

This phrase is not an explicit divorce pronouncement but rather an implicit one (kinayah). Therefore, if you did not intend divorce by it, then it does not occur. However, if you did intend divorce by her going out with you at a specific time to a specific place, then her going out with you does not cause divorce to occur. Nor does divorce occur by her going out after that day to the same supermarket or any other.