Legal Aid isn't that easy to get these days, you wont simply get it with an accusation.Police didnt convict me of anything, she for sure got legal aid regardless i dont know how.
what is CA hearing?
If you think she has got Legal Aid from an untrue accusation you can challenge it.
You need to raise it to the NM hearing the accusation is untrue and being made to thwart your Family Court, i would raise the fact why she is allowed Legal Aid to make the application too when you have never been convicted, arrested for any incident.
I did my NM application against my ex myself, she turned up with a solicitor that cost her £3k who quite frankly was an idiot and i ran rings round her.
CA, Child Arrangement, its what you will get from your C100 application.