I read the other responses---some are polar opposites!
Every family is different. Some families have different boundries. You have the right to say no to anything you are not comfortable with. Your discomfort may not be a matter of not trusting your sister-in-law or niece, but a strong sense of home security and privacy. If you and your husband present the issue as "we don't give our house keys out for any reason, to anyone", I don't know why there should be any personal offense taken. Your niece should keep her cell phone and a whistle with her, and be familiar with the area. She could phone or knock if she needs anything. Her mom is probably just nervous about her daughter being apart from her for the first time.