Gary Chapman has some deep understanding of how couples can reconcile after challenges. Below he talks about trust. I previously promoted his book on the five "Apology Languages".

Can Trust Be Reborn?
 
by Dr. Gary Chapman
 
Can trust be reborn in a marriage?  Yes, if integrity is reborn. 
 
Trust dies when deceit is born. When you lie to your spouse in order to cover-up some behavior, you have taken the first step in killing trust. A few more lies and trust will be destroyed. 
 
The only way to restore trust is to confess your sin, ask for mercy, and then recommit yourself to telling the truth. 
 
On the practical level this means that you must establish a new record of being trustworthy. 
 
Invite your spouse to investigate your behavior.

 

Every time your mate discovers your actions matching your words, trust grows. 
 
It takes time, but you can become a person of integrity and your spouse can come again to trust you.