I think what bothers me about this situation has much to do with the conversation the two of you had when got together for drinks.
When you asked her why she was suing you for full custody her response was the children need a "full time" home and she had been the primary caregiver since birth. Prior to the lawsuit it seems you and your W had a pretty decent custody plan in place even if it was informal. She certainly had NO issue leaving you with the children when she was off to visit OM.
If her concern for the children was *so* grave why make the leap to an immediate lawsuit without even approaching you first? IMO she lost total control of you and the lawsuit was her way of gaining it back. It makes ZERO sense that somebody who is a trained therapist (your W) would even think for one second a surprise lawsuit was a good first step instead of a conversation between the two vested parties.
Your W may have been the primary caregiver since birth but divorce often changes primary and secondary roles. It's an unfortunate aspect of divorce but it is what it is.
When you and your W had drinks she lightly glossed over the custody/lawsuit issue and went right to the flirty/kissing/digging for info about your personal life issue. I hate to say this but I do wonder if she was gathering intel on your personal life in case the lawsuit does go any further.
If she felt strongly enough to sue you without so much a conversation or heads up then it seems to me if she "hates" the situation that much way more focus would have been put on the custody issue during your date.
I mean, your W was willing to travel halfway around the world to see OM and thought you were more than suitable to be the primary caregiver while she was having her affair. What changed? IMO nothing has changed other than (A) the OM dumped her and (B) she saw you moving on and realized how much control she had lost. And like it or not those reasons have NOTHING to do with the children and that is very, very sad.
I don't know really. We all want the very best for you.