Is there some place in your community that you can tap into. In our community there is a center for this. I have not idea what it's called, but I know both parties show up and the visitation takes place behind 1-sided windows, so a neutral party supervises it.
The good news is that she is 14 years old...fairly old to choose where she wants to live. Within a few years, she can just tell her Dad that she doesn't want to go if she has other plans...but for now, try asking her friend's parents or anyone that you think your daughter will trust.
The supervisor will have to go to court and bring their observations...so choose someone who is strong enough...