Mate, you are focusing your case too much on your ex and not enough on your kids.
I know it's extremely tempting, but don't fall into the trap of who-can-b***h-out-the-other-best. Parenting cases aren't mud-slinging matches, and to the contrary, parents who go down that path often find themselves losing residency and facing supervised visits long-term because going on a he-said-she-said rant just shows how completely oblivious a party might be to the impact conflict has on the kids and how little insight they have about the child's needs. In what world can the court regard either parent as capable of acting in the child's best interests if they can't even get past their conflict and hostility to communicate and recognise the child needs both parents to be happy?
Don't do what your ex is doing. It's petty, and the court knows it. If she hasn't reported the allegations to the police, if there's no police records of the allegations, and if DOCS haven't been involved, the evidence is just he-said-she-said. Instead, show the court that you're a good dad. Show that you're committed to being a part of the kids' lives, that you're positioned to care for them as often as you're asking, that they have a positive relationship with you. Make the case for a post-separation parenting course to improve communication between you and the mother, respond to the allegations with your factual version of events, highlight that no other incidents have happened, argue that changeovers at school will minimise the risk of the kids being exposed to conflict.
Don't underestimate the impact of a positive case, over a negative case. Parents who b***h out the other often find themselves on the losing end, so try not to be that guy.