@Babuchak
You are an odd family.
That's very rude. Why is OP and her family odd?
The whole thing is odd, but some posters are completely over-reacting. "borderline child abuse"? FFS, get a grip. A 12 year old is more than old enough to spend the evening home alone.
Have you RTFT? It's not his home! His cousin was supposed to provide childcare, OP sent her son there in good faith, where her niece proceeded to ignore her DS the whole evening and said one sentence to him. Yes, that can be 'borderline abusive', especially as OP has said this is not a one-off. You may not have experience of this, but a child does know when they're being treated differently. My aunt let her daughter target me in her home as a child, to get back at my mum. Just because you don't understand something, does not mean it is not possible. The niece could very well be trying to get at OP.
I would happily leave my nieces and nephews and my own kids alone at that age, but because we are normal, and close, nobody would mind.
Would you also ignore your niece/nephew all night? Doesn't sound 'normal' or 'close' to me?
As per my previous post, I would stop the babysitting completely.