Welcome, though sorry to hear of the struggles that bring you here.
It can take a long time to clear the wreckage of our using. And maybe just as long to gain back the trust lost because of our missteps. I don't think there is much you can say to convince your wife of your innocence, you have to prove it with actions...with staying clean even in the face of this loss of trust.
Try to understand what she's going through. The fear of a relapse, her child's father in active addiction. You know you're not, but the fear it still there. And she probably has her own welfare and that of the child foremost in her mind.
You might share with her what you told us, that she is the reason you are clean and sober and that time will show that recovery is your priority.