Is it considered a form of disownment and disbelief that atones for sins —and we seek refuge in Allah Almighty— for one to pray Isha while resisting the urge to urinate due to tight clothing, recalling the Hadith: "There is no prayer in the presence of food, nor when one is resisting the two impurities"?

The obsessive thoughts you mentioned do not expel one from the faith. As for performing prayer while suppressing the urge to urinate, it has been prohibited in the hadith: "No prayer in the presence of food, nor when one is suppressing the two impurities (urine and feces)." The majority of scholars interpreted this prohibition as karaha (dislike), and that what is negated is the perfection of the prayer, not its validity. They consider the prayer of one who is suppressing these urges to be valid, except that the Malikis deem the prayer invalid if the suppression of urine is very severe, causing hardship and lack of concentration (khushu'). However, a mere feeling of the urge to urinate does not incur karaha. In summary: praying while suppressing the urge to urinate is makruh tanzihi (mildly disliked) due to a deficiency in khushu', but it is valid.