Oh my gosh, Blue! You are a super hero, do you know that? The stuff you have to deal with boggles my mind that you are even awake right now....
Okay, so, I think that because your cousin is using the money of the business to go on a non-business related adventure... you have legal grounds here to stand on. I know you probably don't want to hear that. But... there is a time when you have to seperate business from family. You love her as your cousin and you need to deal with her issues of BP seperately from the issues of the business. Perhaps madatory in-patient treatment or there will be consequences like being fired? I know ADA, but it clearly states that the employee cannot be causing direct damage to the business that is a hardship on the business - like galavanting across Europe on the company dime... I mean... she's a co-executive but she can still be removed. Also... using company funds to travel for pleasure is white collar crime...

What would she do if you froze the business account right now?
How stable is her husband? If anyone gets those kids, he is the one. I know for a fact that dads get their kids (I have 0 custody over my oldest son,) as long as they are stable and employed. And things like a suicide attempt in front of the kids.... she is so lucky she doesn't have CPS on her right now (I'm guessing she doesn't or you would have said...) But, I suggest you band together with her husband as the 'this is not okay, and unless you get treatment you can't see the kids,' because sadly her behavior is damaging to them.
I wish I had more advice, but... to save your business you may have to become the bigger boss. To save your cousin you will need to bully her into treatment...

All I know is that business can rip a family to shreds... I don't want to see that happen, but you can't survive this way.