Other people's animals (and wild animals, too) is a big issue with me. I just find it deplorably irresponsable for people to allow their pets to run loose. Dangerous for the animal, and can cause so much damage to the neighbors.
I have no problem at all catching an intruding dog or cat, and then calling the pound to come get it. Those places keep the animals for a week or so, so your neighbor will have a chance to get her pet back. But that will be a lesson learned, and hopefully she will keep the dog in her yard, or on a chain, from then on.
Oh, do be sure to talk to her first - I think you said you've already done that. Since you've covered your P's and Q's, I say, go ahead the next time the dog comes over, grab its collar, put it in the garage, and call Animal Control.