I started boarding in Y10 (but not overseas). I loved being at home, longtalljosie, but our local schools were awful and I was reduced to tears on a nightly basis so, for me, even at 14 I knew I had to make a difficult decision and I was fortunate that my parents supported me. I was happy boarding in terms of pastoral and educational welfare, but when I was at home I was a nervous wreck from Sunday night to Friday evening which is no way to live a life.
I made friends quickly, but was certainly aware that I was the 'new girl' for quite a time. It is possible that the discomfort comes from your friend's daughter, rather than her peers, and that is perfectly natural. I saw my parents often, and spoke to them regularly (I appreciate this isn't always possible).
My best friend started boarding in Y9, and we quickly bonded, but all the staff commented that she was much happier when I was there. I don't mean that arrogantly, just that once she clicked with someone everyone saw an instant change in her happiness. She told me how much she hated Y9: her parents told her to stick out the year and then decide. By having an end in sight, she was happier, but equally by the time the year was up she had settled better.
My sister was miserable for the first two terms. It does take time. Some people are ready to board earlier than others, some will never be ready. I think she needs to stick it out, if only for the year, then chalk it up to experience and move on. She's 14 - old enough to be miserable (and yes, to be affected long term by it), but also old enough to know she is nearly 1/3 of The way through the year now and the worst is over. They'll be ramping up for Christmas soon and that is a lovely distraction.