Diverticulitis: This condition involves inflammation of a diverticulum in the digestive tract, most commonly in the sigmoid colon. Improvement with defecation can occur due to the temporary reduction in pressure within the colon. The right lower quadrant pain can be referred from the sigmoid colon due to the complex innervation of the abdominal organs.

Irritable Bowel Syndrome (IBS): Although IBS typically presents with abdominal pain, some patients may experience lower back pain. The improvement with defecation is consistent with IBS, as bowel movements can relieve the abdominal and referred back pain.
Constipation: Severe constipation can cause lower back pain due to the increased pressure on the spine and surrounding muscles. Defecation would relieve this pressure, improving the pain.
Hemorrhoids: Large hemorrhoids can cause significant discomfort and pain, which may radiate to the lower back. Defecation can temporarily relieve this pain, especially if the hemorrhoids are reduced during the process.

Appendicitis: Although appendicitis typically presents with right lower quadrant abdominal pain, it can occasionally cause referred pain to the lower back. The improvement with defecation is not typical, but appendicitis is a surgical emergency that must be considered.
Kidney Stones: A stone in the right ureter can cause severe lower back pain (renal colic) that may improve with changes in position, including the act of defecation due to the movement of the stone.
Ovarian Cyst or Torsion: In females, an ovarian cyst or torsion can cause lower back pain that may improve with position changes, including defecation. These conditions are emergencies and require prompt diagnosis and treatment.

Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can cause chronic abdominal and lower back pain. Improvement with defecation might be seen, but these conditions are less common and typically present with other symptoms like diarrhea, weight loss, and abdominal pain.
Spinal Pathologies: Certain spinal conditions, such as a herniated disk or spinal stenosis, can cause lower back pain that might improve with position changes, including defecation. However, these conditions are less likely to be directly related to the act of defecation.
Neurogenic Causes: Rare neurogenic causes, such as a tumor compressing nerves, could potentially cause lower back pain that improves with defecation due to changes in intra-abdominal pressure. These are rare and would typically be associated with other neurological symptoms.