I need some perspective please.
Half sibling is staying with us a few weeks over Summer Holidays as both live far from each other, get on well (or so I thought) and I am trying to encourage a strong bond between them as both are and will remain only children. Both girls share same Dad, I'm Mum to the younger sibling. Both children no longer live with Dad but see him on a regular basis and I have a good relationship with their DF (we split up when DC was an infant and I've since remarried). The older one stayed last year, is now entering her teens, very sensitive to any kind of criticism and hormonal (although if I'm honest she's always been like this, it's only magnified now). It's worth mentioning too that the older sibling constantly professes her love to the younger sibling and is always wanting to cuddle and kiss and be close (which can irritate the younger sibling at times). Her family don't have much money but she saved up and brought us all gifts and photos she'd collected from us which I thought was a really sweet gesture. So shes generally a nice girl and has been looking forward to coming to ours for months now, we are also taking her away on hols next week and try and do activities everyday when she's here.
She has been here a week now and has extreme bouts of moodiness anytime I say anything that she mildly disagrees with, she tells me or is implies she wants to go home. It had started to really irritate me yesterday, she did it again whilst we were having dinner, so I said to her I find her constantly telling us she wants to leave annoying and if she wants to go I would find it sad BUT no one is forcing her to stay - her mood and attitude darkened and so I sent her to her room. I've addressed this with her DF over the phone, who has spoken to her DM and I've made it clear that if she wants to go home, her parents can organise this at anytime. She doesn't want to apparently now and has apologised. She's also having problems with her mum, her mum has MH issues and apparently her mum is finding it difficult to deal with her behaviour and has taken a huge step back and seems quite disinterested (worth mentioning that apart from a coffee or two together I don't really know the mum and am more in contact with DF). So, I could deal with all of the above but then the following happened.
My daughter witnessed her half sister acting like this and also how I spoke with her sister during and afterwards and how she apologised. As I tucked DC in last night she asked what would happen if her sister acted like this again. I explained that she hopefully wouldn't now that she's spoken to her parents and apologised. I asked my DC if she'd like her sister to stay and she replied with kind of. They went swimming yesterday and were together in the water hanging out. After a while my daughter removed herself from her sister, sat in the shallow pool and shouted over from the water to me that her sister poked her "butthole". I was sat in the cafe not far from waters edge, with lots of people around. DD has form for being loud, overtly confident and tbh a bit rude at times. I found it a really odd thing to say and if I'm honest a bit embarrassing as lots of other parents were sat in the cafe too. I was about to respond to DC and then older sibling joined her in the shallow pool, my DC then quickly shouted over to me that she was only joking before I could respond. Well, last night she told me that she wasn't joking and it actually happened in the pool, apparently it was over her swimsuit material and made her feel uncomfortable. My DC then mentioned an incident that happened last year that I was unaware of, apparently my daughter was sat on the side of the bathtub and her older sister pushed her into the bath. My daughter didn't like it and I wasn't aware of this. I've explained to my daughter that both incidents are completely out of order. She doesn't want me to talk to her big sister as she will call her a baby. It's kept me awake last night. Older sister is 12.
I've no experience of dealing with siblings so need help here. Do I sit her down and tell older sister this is totally unacceptable and she needs to apologise to her younger sister. Do I send her packing today. I don't feel comfortable leaving them alone in the same room now. Her home is a 7 hour train ride / days worth of travel away so it's not like I can drop her off there (so will need coordination). Please help !