Have you talked to your DSD about it? I would just forget SIL & ask DSD why she wants to go to these schools. Being Catholic won't have a huge impact on weather she'll be accepted or not, but her previous behaviour will.
Tell her all that. Tell her that they won't accept her if she doesn't pull her weight. She has to be up to their standards or she'll end up in one of the government schools anyway.
Maybe she wants to be somewhere where they'll be stricter with her & push her to push herself? Maybe its just about trying to look good.
I'd be finding all this out from DSD before you go any further & explaining to her all your reasons for not thinking its a great idea.