I understand how hard it can be to screen out a problem person, and then later avoid dwelling any interactions with them. Hopefully you can decide on an attitude and a strategy for keeping your mental distance from her while at the barn so that you get your barn time back at your convenience.
What relationship does the barn owner have with the pesky non-boarder? Do they interact, are they friendly, is it just cordiality or are they truly friends?
Let the barn owner know, quietly, of your allergy to the pesky non-boarder. The point you want to make is that the PNB is an incentive for you to leave the barn, when otherwise you would stay. The barn owner needs to know that the PNB is a problem in their business. If you feel this way it could be that others do as well.
Problem personalities can cost a business customers, even employees. It is costly to recruit and onboard new customers and new employees, as well as the disruption to the business. But business owners and employers can’t know what the problem is if no one tells them.
What is your trainer’s relationship to the barn and to the pesky non-boarder? Is the PNB also one of her students, and/or does PNB ride horses for the trainer? If so then it is worthwhile to let the trainer be aware as well, as she could possibly be equally affected by the PNB’s problems with her other students.
Keep the message factual, short and to the point, with some empathy for whatever it is likely to mean to the person hearing it. It may not be pleasant, but you can do this and defend what is good about your horse life. Good luck! 
One time in my long career as a boarder there was a fellow boarder who pestered and annoyed the bejesus out of everyone else at the barn who had contact with her. For me, that was seldom as I was not there at the same time of day that she was, except for a few encounters. The lady had been kicked out of a series of other barns and the barn manager at this one took pity on her and her horse. However, the horse was clearly in charge and living extremely well, so we ran out of sincere sympathy for him, while cheering him on (he led her around, rather than she leading him). After many months of being good sports, the three boarders who had the most contact with this lady went together to the barn manager to say that they couldn’t take it any more and were leaving to get away from the problem lady. The barn manager was also at the end of her rope and gave the lady notice to be out in 30 days, so the other boarders would stay. It was a lively 30 days and the barn manager had to haul the horse to the next farm owner willing to take the lady to get her out, but at last she was gone. From a distance the situation was kind of funny as this problem personality was so outrageous. And yet, even with my limited contact, she is the only fellow boarder that I ever did as the OP did - saw her car, changed my plans and headed the other way to avoid her! Just once, and it wasn’t long after that the lady was kicked out of this barn, thus maintaining her unbroken record of boarding barn failure. 