Good discussion

Some comments on various details:
I guess I can somewhat see why you are saying the first response invalidates her feelings, but if I felt my husband would cheat, I'd love to hear "I'd never cheat on you". In that case, I'd want my feelings or fears to not be valid, and I actually used to wish that he'd say exactly what you said.
well you want, you are able to regulate your anxiety and this is all good for you. A pwBPD however won't be able to do that so when the "I'd never cheat on you" comes the pwBPD will not be able to sense your sincerity but will perceive a misalignment, conflict and will only get more anxious.
Me: I understand your worry. You don't have to feel so unsure because I love you very much and cheating on you is not something I would consider. I am going purely for business and you can reach me by text message if something urgent comes up but I will call you *** (when convenient) to let you know I'm thinking of you.
"I understand your worry" is a bold claim. It is however not demonstrating understanding and can be invalidating. The "purely business" is unnecessary reassurance and may only raise suspicion. The text and phone is problem solving, too early at this stage and may benefit from simplification. It is a good idea to have some regular communication pattern - one with enough leeway to feel not on a leash when away - you have needs too! But first and foremost comes validation and communication promises are us providing some (weak) soothing where the pwBPD should do the self soothing of the core trust issue. By offering a solution we take the ball into our court when we should leave it in theirs. Leaving the ball in their court is hard. Exercise: Bite on your tongue at the end of your message
When it comes to validation it is often best to
- avoid "I"
- be brief
A good starting point is to consider the situation from an emotional and practical perspective of the pwBPD:
- anxious
- history: Been cheated upon before etc...
- jealousy
- lonely
- other current stress factors
- self image
What is also important is whether this is a on-off problem or we are dealing with a constant nagging. Most likely it falls into the second category so not only do we need a response but we need something that works well for the next trips and as a broken record and with a boundary.
Most likely too strong: "This trip I don't have time cheating on you, I'm too busy cheating on my other 3 wives." <bite tongue before opening mouth>
Maybe better: You are struggling to trust me. It certainly is not nice to be alone at home and anxious. <bite tongue now>
Her (escalating): You are planning to cheat
You: You had bad experiences in the past with X. You struggle to trust me now. I'm not cheating but I can not and will not prove it as this is impossible. My job requires travel. It requires me to be away and being with me it requires you to trust me. It is hard for you.
<this is trying to normalize, provide personal context etc. Not too complex as complexity breeds suspicion. It needs to be obviously true with no need for defending. It may or may not be heard >
Her (obviously not listening): I don't believe it
You: You struggle to trust me. This is your problem. <repeat as needed, preferably exit the stage asap.>