Babies sense tension. If you are tense when your MIL is around, your baby will sense it. If you are anticipating the reaction she has, you are stressing. The one thing to remember though is at 4 months, you don't force her to stay with someone. You take her back and soothe her so she knows you are there to protect her. At that age, you don't teach lessons and you don't leave her in a situation where she is frustrated. She will get to a point where she will be fine with your MIL, but right now she is learning you are always there when she needs you and bonding. After about 7 months of age, you can try letting your MIL figure it out, but not now.