We recently adopted a stray border collie/lab mix that showed up lost
at my dad's house. His Newfoundland attacked her with full intentions
to kill her. We were not able to locate her owners and she couldn't
stay at my dad's.

She seems to be very intelligent and well trained. She usually only
needs to be corrected once. She doesn't have a strong herding
instinct and works very well with the kids. The only problem, she is
very sensitive and if she feels neglected or thinks she is abused, she
jumps the fence and takes off. We gave her a bath and found out she
hates water (felt abused), off she goes. She also will take off if I
fail to walk her at least twice a day. We have a 1/4 acre yard, she
has plenty of room to exercise and she prefers to be outside.

She never goes far, and seems to return on her own, but in a busy
city, this is dangerous. She knows her boundaries and only takes off
if she is punished or doesn't get her walks.

Would an invisible fence help keep her contained? Or is there
something I can try with training. My fear with invisible fence is
that she would perceive it as punishment and take off for good.

Thank you for your suggestions.