Personally to me it's no different from a group of kids being presented with a stethoscope.
Every single one of those kids will want to put it in their ears and see what they could hear.
Kids are inquisitive. They ask questions.
Op doesn't know the full situation around what happened.
I would have no issues with my kids wearing any kinds of national dress from any other country. But it seems even the thought of trying on a turban or a kimono might be indoctrination in some people's eyes.
My kids would try it on and laugh about it. Not respectful to the country involved but anyway.
In a couple of weeks they will be wearing Halloween costumes again something not commonly done in my personal culture.
Then after they may attend some Chrsitmas events again not common in my culture.
I don't see any of these as indoctrination, and am comfortable with my kids being exposed to other cultures and ways of living.
I really think Op seems to be confused about what actually happened. But I think she also need to think about what she is gonna do.
Because if her kid is spending every other weekend in a household which may fully be Muslim now- unsure if her Ex has converted. She will see people.praying daily. She will notice the different food available. Different ways of dressing.
She may be invited to Eid celebrations watch people fasting etc.
All of this isn't indoctrination- it's just someone living their life with a child observer.
What she gonna do next- when the new partner is fasting and her daughter asks to try it??? Again accuse her of indoctrination???
Short of banning her kid from going there she can't stop her from being exposed to a person living their life and practicing their religion.