LP Gosh this is a tricky one...everything about it screams WRONG! There sounds like there's a real "you vs us" dynamic going on which is a really hostile and unnurturing place for someone of that age. My DD is nearly 12 and yeah we have our dramatic moments (fully understand with the slamming doors etc, sounds pretty normal to me) so I'm pretty perplexed as to why the toys and eating would warrant such a level of scrutiny. Are there any concerns re eating disorders that they are trying to catch her out on, or is a just a general distrust of how she's spending her time and whether she's telling the truth? Really, if they're that uncomfortable leaving her at home by herself after school, then perhaps they should make another arrangement so she has some company and/or supervision. That is IMO a much better solution than video monitoring!!!

I really don't know what advice to give...perhaps start by discussing it with your bro and mum...try to use non-confronting language but say how horrified you yourself would have been, then maybe suggest some creative alternatives, in terms of managing her time after school (ie can some other family members or friends share that role, or maybe some of her friends have a parent at home in the afternoon).