I am so sorry that your wife could not see the good in supporting you.
My husband and I have been married for 21 years, almost 22 ;-) now, In the beginning there was a lot of acting out but I LOVE him and I PROMISED in my vows, to make it work. When the discovery came out almost a year ago it did NOT make me question my vows.
I empathize with your situation, no matter what happened between you and your wife it is wrong for her to keep your kids away from you, seems to me she needed an excuse.
I am sorry.
"Believe in someone, trust yourself."