OK - hang in there, it is very, very early days. DD1 started at her boarding school when we were still overseas, a few weeks before we relocated to the UK. She was the most miserable child on earth for the first 2-3 months. She was (and still is) a weekly boarder, but had to spend the first three weeks of term at school because we were still packing up and moving back. I had (wrongly) thought that this would be a good time for her to bond with her dorm mates, but in reality, most of the expat parents stayed in UK for a few weeks, so on two weekends, she was practically the only one in the dorm. We had tearful phone calls, all of which started with "I hate it here. Can I come home?" The texts and IM and skype calls were as bad.
It improved when we were back in UK (I realise you are going in the other direction, so this isn't helpful!) - I would sometimes pop down on the train after work and take her out to dinner midweek, and she came home at weekends. How many exeats are you going to be able to manage before you leave the country? Is there any chance you could stay behind for a little longer, so she could have a couple more with you, while your DH and DD2 head off together?
She has now been boarding for two years. I would say she is still not entirely, 100% happy, but she has a good group of friends, both boarders and non-boarders, and some weekends chooses to stay in the dorm, if they have fun stuff planned, rather than come home. The beginning of this term did not start well - we got back to the "I hate it here and want to come home" calls. This was largely because she had an accident and had to have an operation, so missed the first boarding induction weekend and first week of school, and couldn't participate in the outward bound activities of the second. Things are now better, she chose to stay in the dorm last weekend, and we seem to be back on an even keel.
I think you need to give it six months. When we got to six months, I felt that it was going to work out - the "I hate it here, can I come home" start to every phone call was followed by a laugh, and telling me what she had been doing. If she is still as miserable as sin, pull her out, and either send her to the local school where your DH is posted, do the online high school, or stay in UK with her and your DD. Is there any chance that your DH could pull out of his posting, and come back to UK, so that you could all be together? I realise this might harm his career, but sometimes you need to put your family first (we have taken the decision to stay in UK until DD1, at least, has finished her education). Or, you have lots of supportive family in UK - how about a school near where they live, where she can board weekly and see them at weekends? (DD2 boards near her grandparents and sometimes goes to them for the weekend, which she loves.) I think full boarding schools can be a mixed blessing - on the one hand, everyone is in the same boat, on the other, it is full on boarding, with no escape to a little bit of home life.
Anyway, good luck!