First…your kid is applying to college. There is no “we” or “us” in this application process.
I’m guessing you don’t mean Benard, but mean Barnard, is that correct?
My opinion…Barnard would be a reach. But you never know. University of Maryland…apply early action or it’s very much a reach. Babson, a match in my opinion. Same with Union. Lehigh…hmmm. Not sure.
Why Cooper Union?
Your first list posted here looked very balanced to me. Some reaches, some matches, some sure things.
University of Delaware is worth a look see.