Is it abnormal to have vaginal bleeding in between periods and intense abdominal pain?

Not normal: No, this is not normal. Bleeding in between periods could be caused by many things - a polyp, infection, or a hormonal imbalance. But if it is also coupled with severe abdominal pain, you should see a doctor right away, as this could be something very concerning like a ruptured ovarian cyst, ovarian torsion, pelvic inflammatory disease, or even something non-gynecologic like appendicitis.