Is the belief in the obligation to divorce one's wife correct? And does intentionally abstaining from prayer for two or three days, and engaging in marital intimacy with the intention of enjoyment before separation, constitute apostasy? If so, what is the ruling concerning the wife and how can she be brought back?

The belief that it is obligatory to divorce one's wife due to obsessive doubts (waswasah) is incorrect. Rather, one must completely ignore such obsessive doubts in their entirety, as Satan seeks to sow discord between spouses. Abandoning prayer is one of the greatest sins, but it does not lead to apostasy according to the majority of scholars, unless it is done out of denial [of its obligation]. Furthermore, cohabiting with one's wife while believing it to be forbidden does not cause apostasy. Therefore, your wife remains under your marital bond. What you fear concerning disbelief and divorce are mere obsessive doubts that must be ignored. Seeking Allah's help and making supplication will aid in getting rid of them.