I recall some years ago seeing a show on TV about phobia's. They said that phobia's about clowns and other kinds of characters while not uncommon, is not that unusual. Some never out grow, some do.
The one thing about it was my daughter decided on her own to overcome her fear when she saw a Barney outside a video store posing for pictures with kids. She really wanted to do that, so I turned the car around and gave her a chance with encouragement from me that if she felt uncomfortable I would take her away instantly upon her word. She was very brave but you could see just how uncomfortable she was. While I consider what she did a brave thing, I also understand some simply do not get over the fear, the same I have with large dogs, well mostly any dog that I do not own.
So, in short I understand and would be the first to acknowledge your rights to be afraid and I respect your fear. I have always tried to hide my fear of dogs from my kids as best I can and like you tolerated many dogs for my kids sake. Hopefully your daughter will outgrow her fear, but if not well I suspect she has a mom in her corner.