Pale Emperor - I agree with the others here to encourage your ex-wife to keep looking into and researching her doubts as it seems she really has those doubts about the WT Society - but guard your emotions and guard her possible ability to try to manipulate you back into a romantic relationship. Especially if you've already moved on.
The problem is like some mentioned that your ex-wife is really concerned about what her JW friends and family think of her - so her confiding in you about her doubts - although positive for her in and of itself - kind of puts pressure on you to keep that confidential for her as you see her waffling back and forth in regards to pleasing her staunch JW elder dad and family - and - at the same time trying to raise your daughter with you in a co-parenting situation.
Years ago I dealt with an ex-JW wife who was more fanatic than yours- but turned our teenage kids at the time against me. Another thing you have to watch carefully. Pay attention to what your ex-wife is telling your daughter and what your ex-wife's parents are putting into your daughters head - then take a deep breath - and be happy you have a new girlfriend who shows you support.
There are so many variables here that it's impossible for anyone to tell you what to do- but the need to be smart, cautious, and follow the old adage " fool me once shame on you, fool me twice shame on me " seems to possibly apply here in this situation. Your ex-wife is in a very fragile emotional state waffling between pleasing her staunch JW parents and raising a daughter with you. Just be careful my friend, think and proceed with caution. Hang in there, we're here for you as friends and a support no matter what you do