Am I spoiling my 8 1/2 month old?

When my son and I visit my mother, (every week or two) sometimes he cries and screams while she is holding him, but then when I take him he calms down. He even reaches his arms out to me so I know that what he wants is me. My mother gets angry about this, says that I am giving him the message that I am "rescuing" him from her, and that I am spoiling him. I have tried to explain that it is separation anxiety/stranger anxiety, but she thinks that is a crock. AM I spoiling him?