I am familiar with a couple that divorced recently with 3 kids and the father DID get Legal and primary custody AND he travels all the time. I can't say that I think his wife had a mental illness (she may have) but she was definitely partying really hard.
This came about due to psychological evaluation I think they both had to submit to it and it took about 4 to 6 months of meetings and testing of them both. The husband had to pay for it because he was claiming her unfit - it was expensive - but it resulted in his favorable custody arrangement.
Wishing you the best with this your wife does sound like she is mentally ill.