For money and assets? Outside of child support, whatever. It's not worth fighting over.
What I asked for was two tiers of supervision. If I couldn't get X, I wanted Y. My lawyer kind of hemmed and hawed about it, but I knew (see, this is where trusting your gut becomes so important) that unless my ex was really working a program, his failure to follow through would shine. Point blank: he starts stuff, but can't sustain anything. It's his super power.
What they instituted instead (with the help of a GAL) was a period of supervision (only three months!), that we split payment for, so he would show he was really invested in working a program and capable of having unsupervised visitation. He failed to show up to appointments immediately and the court was notified. They haven't made the official recommendation yet for how to proceed going forward, but it can't be good for him and his unsupervised request.
Considering your STBXAH's history, my direct requirements for CUSTODY would be:
* Joint custody is whatever. If that's the sticking point, give it to him. Legally all that means is that he gets a say-so in major decisions, which is so wishy washy it means nothing unless he is motivated to keep you in court for the next fifteen years over things like doctor appointments and their religious training.
* Supervised visitation indefinitely. He is a drunk who is under investigation for molesting his daughters. This should be obvious.
*** This leads to the question of who supervises. His parents? His current or future girlfriends? The court? Who pays for a court-appointed supervisor?
* No transportation. He is a history of transporting them while drunk, which is criminal.
* Supervised visitation SCHEDULE by the state guidelines (do you have these? they're a godsend), provided he meets the supervision requirements. Every other weekend, split holidays.
* No extended parenting times on breaks.
WISHLIST:
* Mandated parenting counseling for X sessions, monitored by the court.
* If he wants to move off of supervised visitation, what would that "proof of evidence" look like?
And really, you're betting that whatever he gets is too difficult for him or gets in the way of his drinking schedule that he doesn't take advantage of it. As they do.