Seems like this is the real question that the OP is asking – does the OP have a realistic chance of admission to Washington University? If the answer is yes, then the OP will apply ED there as it is the preferred choice. If not, then the OP will use ED on Barnard, since there is no point applying ED (or RD) to a college where the chance of admission is zero. (Of course, the same question can be asked about how realistic admission to Barnard will be.)