I would be plainspoken about the addiction being the reason. As Melissa says, it might wake her up. It is enough reason with no explanation necessary. ("You have an addiction" - full stop - is enough said.) Knowing this, you should simply never leave your child in her care. Not even for a half hour, I am sorry to say. What if a freak accident happened and you had to explain to the police that you left your child with her knowing she "has a prescription pill addiction and can be careless sometimes"? Bad enough if an accident happened when you left your child with someone who was not addicted to drugs, but if you knowingly leave her with someone who is, and then a disaster occurs, whose fault is that? Hurting your mother's feelings, or having to go against her wishes, means zero compared to having a safe child.
I agree with you. I wouldn't even let her watch the baby alone, you don't want her to be "high" when your child is in her care. It sounds like she could use some help. But regardless, anything that is said probably will hurt her feelings. I would just tell her that this is your child and you have a plan that you feel is important to follow for raising your child. Or tell her that you do not feel safe keeping the baby with her due to her addictions. It will hurt her feeling, but it may also make her realize that she is going to miss out on her if she doesn't get help.