The way IDEA is written, Child Find is on the school. Schools can & do sent out requests to parents for them to OK a sp ed eval to happen for their child. Has the school done this? The next time the parent tells you they want an IEP, I'd take that as a verbal request for a sp ed eval to be put in motion. (My state, PA, even has timelines on when this has to happen.)
The next time this mom asks for an IEP, tell them that the school can reach out to her but she needs to provide a written OK for a sp ed assessment. That's the 1st step in the IEP process. (It is a complicated process. I know I didn't understand that when I saw my child had needs for sp ed.)