How do you let go of the distrust and NOT carry it in to your new relationship?

Very important question Trevor. In my view the simple answer is time and personal development.

A deeper analysis would require you and any future partner to look at the meaning of trust and the value upon which you both place upon it.

What you may also be feeling and referring to is the pain that can come from a breach of trust and being made vulnerable. We all want to feel safe and secure on many levels so when uncertainty is introduced, change can be suddenly thrust upon you causing a shock to your nervous system and so on. A state we neither rarely choose or can sustain for any length of time.

Once trust has gone it's gone. Betrayal is a very cold blow to anyone.
No matter whether it's a partner or family member, when trust is gone especially for the second time, time to value yourself properly and dump them. You don't need people like that in your life, trust me on this one. There are plenty of other good people around who will better suit with better values, morals & integrity.

It takes time. Both of you presumably will be taking baby steps with being open and honest with each other.