Yes it will continue to work for her, but the mother feels strongly that it should be still available for other children in the same position. If it does go into litigation hell perhaps open source is the answer, let parents build it for the device themselves?

Technically, Apple can remove an app remotely from all iDevies if they are legally required to do so. Whether they will be required to do that in this case is unknown.

I was under the impression that the iOS kill-switch was exclusively for rogue apps/malware.

Has it been used for legally questionable apps before? A bit of Google-fu didn't turn anything up immediately.