Is is okay to pick up a child with a beer in your hand?

Yes you did the right thing. I lost my husband to a drunk driver. If that would of been me. I would of called the cops as soon as he left. Your mother is not much of a person to endanger her grand daughter. And these people only care about themselves if they are acting this way. I would just start making excuses up to stay away from them. It doesn't sound like you will be missing much.