She can't be trusted so it comes down to three options. Stay with mum, come away or stay at a friends house
Stay with mum or come camping, really she shouldn’t miss work and you can not put your life on hold . she sounds like she would be annoying af if she came camping esp if she didn’t want to.
If her mum has an issue with her staying home with her maybe it’s time she moved out, she might learn to respect other people’s homes if she had her own. I would be telling her to start saving bond $ and learn to budget as she will not be left in your home alone.