First I want to say that I really like BTMRR. In fact, I prefer it to Space Mountain if I had to choose one.
DW was NOT a roller coaster person. On our first WDW trip together in 2008, she asked me which was the mildest roller coaster in WDW. I honestly forgot about the Barnstormer. I was going through in my mind EE, PW, RNR, Space, BTMRR. We were standing by Splash Mountain, so I pointed to BTMRR and said that one. She HATED it. Now this was a person who loved Test Track, enjoyed Tower of Terror, Star Tours, Mission Space Green.
It IS a roller coaster. It is most definitely a family oriented roller coaster. It is not wild. But if you really don't like roller coasters, you won't like it.
As far as fear of heights is concerned, Soarin is more likely to trigger the fear of heights.
Have a magical trip, whatever you decide.