Hi, your friend is in a position where her life is changing. A good, supportive friend is an important “resource” more than ever for her now. It sounds as though, her moving in would cause a strain and possibly/likely damage the friendship.
Tell you care about her and are “there” and will help her as needed, but that can’t include her living with you. If part of the reason she is moving to your area is to be nearer to her family-why can’t they take her in ?
She may be disappointed when you say no but I am sure she can figure out alternatives. And likely your friendship will survive once she has a plan. (you can help her with ideas ) If you allow her to move in you will resent it/her and then you will end up having to suck it up or ask her to leave. She may not even want to go after the agreed upon 4 months, even if you did try to help by letting her stay.
You already have a housing plan ( the moblie home etc. ) in place for yourself and your daughter. Stick to that.