LabCorp review: Blood draw for babies

Today, I visited LabCorp for the Anemia blood test for my 1-year-old child. To my shock and despair, it turned out there were 3 adult nurses surrounding us to draw the blood, and they tried to draw blood using his arms. One of the nurse picked his one arm and then went on to grab the next arm to which I questioned why is his second arm being picked to which they said that since they didn't get blood from his other arm, they want to try the other arm. They then did not pick the other arm saying there is too much movement by the baby, so they cannot draw blood today and that he can come next time. My question here is, was drawing blood for a baby using his arms correct and that if the blood could not be collected the first time then was it correct to then try to pick his other arm. Also, they did not feel obliged to let me know as to why were they using his other arm for and only answered me after I questioned. Nothing of this felt good. I am very surprised that why are we being told to go to such centers for babies.