What do I do if the baby I sit for clings to me when mom comes home?

It's normal. When this happens with my kids, the usually sitter gives a quick hug to our baby, and then hands him over without any fanfare or long goodbyes or drama. Very businesslike. If you and his mom put on a dramatic show, the kid thinks it's a dramatic event. And even if he does cry, it's normal - he's obviously formed an attachment to you, which means you're doing a great job!