First, I want to say it is definitely not your fault. It has nothing to do with training. It'd be like saying a kid with ADHD is because of a poor education. Some dogs are just like that.

Daphne can be dog agressive sometimes. The best thing to do is not put her in a situation to be dog agressive. Try to take her for a run where there aren't other dogs... things like that.

I know you love Josie very much and she is a wonderful dog! Give her a big hug for me.