Fact: The umbilical cord runs between your placenta and the baby's umbilicus (stomach area). It is not connected to your arms in any way shape or form. The baby's cord will be around the neck at about a third of all births. This is caused by the frequent twisting and turning that babies do in the uterus before birth.
If this were true you would be unable to do much of anything in pregnancy, from caring for a toddler in your second pregnancy, exercise or other daily tasks.