Tumor recurrence or metastasis: Given the patient's history of stage IV colorectal cancer, the most likely cause of her right lower abdominal pain radiating to her back could be a recurrence or metastasis of the cancer, possibly involving the liver, kidneys, or spine, which are common sites for metastasis.

Intestinal obstruction: This could be due to adhesions from her previous surgery or tumor growth causing a mechanical obstruction, leading to abdominal pain.
Infection or abscess: Post-surgical infections or abscesses, especially in the context of a recent move and potential changes in medical care, could present with abdominal pain and fever.
Kidney stones: While not directly related to her cancer, the radiating back pain could suggest kidney stones, which are a common cause of severe abdominal and back pain.

Bowel perforation: Although less likely, a perforation of the bowel due to the tumor or previous surgery would be an emergency requiring immediate surgical intervention.
Pulmonary embolism: Cancer increases the risk of thromboembolic events, and a pulmonary embolism could present with sudden onset of chest pain, shortness of breath, or in some cases, abdominal pain if the embolism affects the lung's ability to expand properly.
Spinal cord compression: Metastasis to the spine could lead to spinal cord compression, presenting with back pain and potentially neurological deficits, which is a medical emergency.

Primary or metastatic tumor in the pancreas: Although less common, pancreatic involvement could cause abdominal and back pain.
Retroperitoneal fibrosis: A rare condition that could cause abdominal and back pain due to the formation of fibrotic tissue in the retroperitoneum.

Complete Blood Count (CBC): To evaluate for signs of infection or inflammation.
Basic Metabolic Panel (BMP): To assess renal function and electrolyte balance.
Liver Function Tests (LFTs): Given the high likelihood of liver metastasis in stage IV colorectal cancer.
CT scan of the abdomen and pelvis: With contrast to evaluate for tumor recurrence, metastasis, intestinal obstruction, or other abdominal pathologies.
CT scan of the chest: If there's suspicion of pulmonary embolism or to evaluate for lung metastases.
MRI of the spine: If spinal cord compression is suspected based on clinical presentation.
Urinalysis: To evaluate for kidney stones or infection.

These tests will help narrow down the differential diagnosis and guide further management.