How can one distinguish between a tribulation and a punishment in the misfortunes that befall them, especially after committing a sin and repenting from it? And is the separation from a husband who became ill-tempered considered a punishment or a mercy?

A person cannot know whether what befell them is a punishment or a trial, and knowing that is not important. The statement that a Muslim's condition after repentance is a trial if it becomes better, and a punishment if it becomes worse, has no basis. However, an improved condition is among the signs of accepted repentance. Your separation from your husband may be a blessing. If you repent sincerely and your condition improves, this is good. It is not permissible to describe the husband as a hypocrite, as this falls under using offensive nicknames, which is prohibited. However, if you find in him overt characteristics of hypocrisy, such as lying, then it can be said that he possesses a characteristic of hypocrisy.