One of the most difficult things that many of us non-BPDs go through are the accusations of infidelity. For myself I don't give them too much attention. For instance if my pwBPD begins to make little jokes or hints about me cheating, then I will calmly address it with something like,
"I know that's a scary feeling to have, but I'm not cheating and I don't like to be accused of it." And I leave it at that. I've learned that the bigger deal I make of it, the bigger an issue it becomes.
We have a lot of great workshops on the right side of the page. You can learn a lot about your relationship and how to communicate better with your pwBPD. Here's a link on one of hte workshops on how to handle accusations:
https://bpdfamily.com/message_board/index.php?topic=87204.0