How do you address issues that challenge your trust?
I think what this question means is this: When your other half does something that suggests or shows they have done something I do not like, what do I do?
In marriage, the other person is not my slave; they are not my employee; they are not my servant; they have not undertaken to obey me as the overlord. I am not the superior moral arbiter. It is therefore inevitable that the person will do things I do not like. I likely do things my other half does not like.
Sometimes the person says they will not do something, but then they do, or vice versa. In my marriage, I do not force the other person to make solemn, binding oaths regarding ordinary everyday matters, to which I may legitimately hold them, by force of what? Punishment? Divorce? Death?
Setting aside the above, broad questions, we are left with the questions of honesty and fidelity.
No one is entirely candid and entirely truthful. In fact, full candour and full truth will kill the relationship. If each person told the other they look tired, old, and ugly, when they do (which everyone does, sometimes), that they find the person they can see on the television or the beach attractive, that they are bored or irritated and wish they had never married, each time such a passing thought crosses their mind, that the other person annoys them each time they do, this would spell disaster. Anyone wishing for total candour and total truth has no idea what they are asking for and is inevitably the sort of person who reacts badly to full disclosure. Typically the only people that are foolish and insecure enough to demand full candour and full truth are quite unable to handle even small doses of candour and truth.
There are situations of fundamental and material dishonesty, e.g. regarding financial matters that affect the household, and there are also situations of actual infidelity in a relationship where the requirement is fidelity.
I have never successfully changed someone's personality or the way they live or behave. If you have, please write a book. You'll make a buck.
When dishonesty or infidelity comes to light, a fundamentally honest and faithful person who has made a mistake, including an egregious one, will firstly know they have done this and will secondly know what to do about it. If they are committed to the relationship, they will be contrite and mend their ways. They will not need explanations or ultimatums. Either they will mend their ways, in which case the problem is solved, or they will not, in which case I have a choice: accept the ongoing dishonesty and infidelity as it is, or leave. Changing them in not an option.
Regarding suspicions of dishonesty or infidelity: I've never met a secure person who worries about whether or not they trust the other person. If someone is fundamentally trustworthy, I trust them. I do not need to monitor or micromanage. If I do not trust them, why did I pick them? If the 'signs' are actually innocent, there is nothing to worry about; if they are not, the truth will probably come out, and probably soon: eventually there will be a major and undeniable slip-up.
In most cases of suspected infidelity I have come across, however, the suspicious person has the demand that their other half find them the only attractive person in the world and not interact in anything but the coldest and most business-like way with persons of the relevant sex. This is the sign of someone who is self-centered in the extreme and desires not a relationship but a mirror, mirror on the wall, who tells them they are the loveliest of all. The other person is of no interest except as a delivery system for micro-doses of emotional morphine to quell the pain of their insecurity. The problem, here, is not the relationship but the insecure person. Such questions should be resolved before even thinking about dating. I was such a person and had no right to inflict my unresolved personality on another person.
One of the first requirements for a successful marriage is the ability to trust a trustworthy person. The inability to trust would disqualify me. I have been in (very brief) relationships with people who are insecure, suspicious, demanding, and reproachful (note that these four characteristics tend to go together as a package deal), and I soon recognised that forming any sort of relationship with such a person was impossible. Intimacy requires trust; no trust, no intimacy; no intimacy, no relationship: just proximity with the enemy.