<p>I think the issue for the OP is two-fold – she knows upfront that the first boarding school is just a stop on the road and she needs significant FA. </p>
<p>If she were honestly interested in the first school and willing to do her best – and then it just didn’t work out, that might be different. The teacher recs might even reflect that: “Susan is an exemplary student and could benefit from additional opportunities”, etc.</p>