Sorry East. There are some books about there about custody with a high conflict ex. Just search those terms.
Mediation works great when you have two reasonable people who are at a rare disagreement and need to work toward compromise. It does not work great when one party is high conflict, because the crucial ingredient (a reasonable person) is missing.
The mediator's job is to move the two of you toward the middle and they only care about compromise. They're not going to tell either party they're unreasonable, they're going to take what they're given and pressure it to a middle ground. The unreasonable person tends to ask for the sun, moon, and stars, and things like weekly inspections of your home. So you're then supposed to give her half the moon, stars, and monthly inspections of your home, in the name of compromise. And thus you are then further victimized by this unstable high conflict person until your daughter is the age of majority.
Consider having your L at mediation. It's going to be the "but I want all of his appliances that I have no right to" and "but I want him to pay for my health insurance" all over again but in matters of custody. Stand tall. If you agree to a high conflict person's unreasonable terms, you will subject yourself to years of emotional vampirism, leaving you unable to be a proper partner (to whomever you are with) and father to D.
Do not fall victim to the "but I'm the real parent" BS. Adoption does not make you a lesser parent. Would you ever look to a couple who adopted because they couldn't conceive and tell them they weren't full parents? No. It's the same for you. Unfortunately, you're dealing with a vengeful person who wants to take from you to fill up the empty black hole inside of herself, which will never be filled. Don't let her do that. Compromise only on matters you find reasonable. If something is outrageous to begin with, put your foot down and do not feel pressured to compromise on it.
Also, be very careful about the decision making pieces of any plan. Do not leave anything loosey-goosey about "parents will decide as arises", because you are signing yourself up for h*ll. Get strict specific terms that don't require conversation because you're starting to see that the two of you aren't going to be able to co-parent. It's looking like parallel parenting is going to be the way to go, since that cuts down on the amount of conflict D has to witness, and it allows you to be a full emotionally-present father to her.
Also, be careful about measures about how conflicts will be resolved. When H's ex found out I moved in, suddenly everything was a problem. She actually wanted to send their D to a boarding school. (That's right, she so wanted her D away from any chance of developing a positive relationship with me, that she was willing to send her away) H said "no" and then his ex said "looks like we can't come to an agreement" and made him go to mediation to "resolve the conflict."
There was no conflict aside from what she'd spun up. She was also rewarded by being able to be in a room with him. He'd cut that off since she used face to face and phone conversations to bully him. So he asked the mediator to put them in two rooms with the mediator going back and forth, to make sure she wasn't rewarded. He also used the opportunity to get a provision in the agreement that mediation could be used to resolve disputes, but the person requesting mediation had to pay for both person's fees. He was willing to do that if something was important enough, and it discouraged her from using mediation to bully him into whatever conflict she'd spun out of thin air.
Educate yourself about high conflict exes and sharing custody. H did not, and it resulted in years of her bullying him. I insisted on some healthy boundaries with his ex when I was with him, and because she hadn't had to deal with those before, she became on a mission to destroy him. Had he not tried to wean her off of him, and rather set solid boundaries, he'd have reached peace a great deal earlier in his life.
Watching from the outside in, I don't think that parents who have an ex who is high conflict and emotionally/verbally abusive realize the toll it takes on their spirit. It's normal to them. But it's not normal to everyone else. D needs you to be present and not living a life of being victimized by crazy. Educate yourself and stand up for yourself and do not feel pressured to compromise on ludicrous things your ex will demand at mediation.