L.D.
Hey Susie,
Listen to your instincts and stick to your guns if the babysitting situation that your sister is proposing doesn't feel right to you. You are the shot caller for your son and sometimes that means making decisions that you know in your heart are best for him but may not be popular with other people. If you say "No," to your sister's request, she'll probably get over her disappointment but if you say "Yes" when your really mean "No," you'll end up resenting your sister and it could end up being a situation where you find out you should have trusted your instincts all along. You only have one shot at raising this boy, so do what you feel is right.
That said, there's really no need for any unnecessary conflict with your sister. Just keep telling her "No," and that you don't feel comfortable with her invitation at this time but maybe later when your son can tell others his name, address and telephone number if he happens to accidentally wander off from your sister. And maybe you can work out some other kind of babysitting situation at this time that feels good for the two of you.
Hang in there and trust your instincts.