A very tough situation, Au. How wrenching this must be for you, after you have tried so hard to be a good husband.
I have to say that, although I have no information about her history, my first thought on reading your post is that she was an alcoholic when you married her. And though you say the "real wife" would never have done what she did in the parking lot, the fact is that the real wife was drinking heavily with an infant in her care and then she was insane enough to get pregnant again. Two babies are now in danger.
The definition of addiction is that the alcoholic cannot control where she drinks, when she drinks, how much she drinks, nor in whose presence she drinks. This will include your helpless children while you are out of the house.
There is no way, personally, I would let her near my babies. Not for a long time, not unsupervised. The infidelity is a problem....but the the danger to your children is major.
Glad you found us.