Mother in law babysitting..

My daughter is learning to recognize people and she doesn't recognize my mother in law. We were at their house and all she would do is scream if she held her. My mother in law asked to babysit Thursday while I'm at work. I really don't know if I should allow it since my daughter doesn't know who she is and has been going through this phase of screaming and crying if she doesn't know who it is and they hold or talk to her. I feel like it'd be kinda traumatic for her if I left her with someone she didn't know for a whole day. Where my mother is her normal babysitter and she knows who she is. Would you let your mother in law watch her or explain to her what's happening and have your normal sitter watch her? I understand she needs to spend time with my mother in law to recognize her and get to know her but I feel like leaving her the whole day with her might not be the best way to do so.