I have worked with families affected by domestic violence for about 20 years. Every situation is different, but generally, if your divorce is affected by domestic violence, the following things will likely apply:
1) Listen to your gut. Do not allow anyone to guilt you with something like, "If you don't stop them now, then they'll do it to someone else..." You are not ever responsible for what another person does. You are not ever responsible for the failings of a system that may or may not be able to document and appropriately handle any abuse. You're not a prosecutor. You're not a mental health professional. You're a person who deserves to be safe. You're a parent. Do whatever you need to do to stay safe and to keep your children safe. Trust yourself and put yourself first. Statistically, after you file for divorce can be a dangerous time for someone leaving an abusive relationship. Stay safe.
2) Abuse only exists for the court if it has been documented by a professional, usually a doctor or a police officer in the early stages of your case, and a GAL or child custody evaluator later in the case. Do not allow yourself to feel like you need the validation of a judge or some other professional to understand what happened to you. There are plenty of situations that constitute abuse that do not fit legal definitions or may not be able to be prosecuted for whatever reason. Do not get stuck trying to convince anyone else of what happened to you. And do not allow an abuser to convince you to avoid documentation. Document and move on. What you say later won't matter as much as the paperwork. And if you don't have paperwork, people who do believe you may still be unable to act, legally. Separate your own truth from the legal paper trail.
3) Litigation will not keep you safe and is often correlated with violence. A disturbingly high percentage of tragedies occurred in connection with court cases. Understand that if you file a domestic violence protection order, you still need, as one prosecutor likes to say "A backpack and a plan." (see link). Whenever you can, just don't respond or ignore the other parent. Document any threats and, if you feel unsafe, go ahead and leave town. It's a myth that you can't move without the other parent's permission. You cannot change legal venue, so you can't move to California and file for divorce there. But most parents who notify the parent of their intent to move out of state during or after a divorce are allowed to move in Washington or other states that follow the UCCJEA.
4) Abusers tend to love the court system. Arguing with you endlessly in court just becomes another form of abuse after you've left the home and cut them off. I've seen abusers file up to nine new motions in a year because they were so thrilled to discover that their target had to pay a lawyer and take the time to respond to each and every one. Instead of wasting your time at home, informally, the abuser will learn that court will take up all your free time and most of your money. Anyone who is prone to gaslighting will also LOVE the court system. Be prepared for absurd interpretations of your parenting plan, arguments that make no sense, and constant threats to go back to court. HOWEVER, it's actually really hard to modify a parenting plan once it's been filed with the court. So the faster you can get your ex-partner to agree to enough provisions to file FL Form 140, the less money you'll spend on gas lighting motions and fights about whether a Tuesday transfer date really means Wednesday when your ex has an extra work shift scheduled. Contempt motions require lawyer fees, too, so after your plan is filed, you can get paid for all the abuser's motions so long as you don't break any obvious rules.
5) Abusers will tell everyone you are abusive (see link above). They will set up Go Fund Me accounts with your name on it. They will tell the court you drink too much, that you're crazy, that their mother thinks you're crazy, and so on. They will ask all of your mutual friends, relatives, and even your child's teachers to weigh in on their side. (For this reason most schools do not allow teachers to become part of an ongoing court dispute). Do not take any of it personally. Vilifying you is another form of abusing you and keeping you close. Most people who are not involved will see through the abuser's attempt to get sympathy. And when you're escaping an abusive cycle, other people who believe your exe's lies are not your problem. Ignore it all. It's just another way to get your attention and try to control how you feel so that you can't really move on.
6) Abusers are people who hurt others and that is all the information that you need to understand the cycle. Everyone asks "But why does this happen." Everyone wants to know how to avoid it in the future, or if there's something they could have done to avoid being hurt. Everyone wants to find a story that makes sense, so they know that they didn't deserve to be abused. I'm not a therapist, but I can guarantee you that nothing you can do can really affect whatever is going on in another person's soul. If someone is able to hurt someone, that's on them. Let them take responsibility for their actions. You have information about what they're willing to do now and you can move on. You didn't deserve abuse because no one does. You didn't cause the abuse or bring it on yourself because no one can really make someone else do anything. You don't need to accept whatever excuse the person who hurt you may dream up. Their choice, their responsibility. Anyone who hurts someone is revealing their own capacity to hurt. The end. Their choice says NOTHING about their target. Some people don't like the way it feels to hurt others and stop. Others keep hurting others. Whatever a person might say about this decision is really beside the point. If someone hurts you, then you know that they are okay with hurting you, and odds are they will do it again. The situation doesn't have to be any more complicated than that.
7) Some truly awesome and amazing people end up in an abusive relationship. Someone who feels terrible about themselves will often look for someone they really like and admire as a relationship partner. The abuser is hoping that all that specialness will rub off on them and make them feel better. When the relationship doesn't help the abuser to feel magically cured of feelings of worthlessness and shame, the abuser might get mad and convince themselves that the special person they dated or married couldn't really be all that special after all - because why else does the abuser still feel like crap?
8) You might be broke. Abusers tend to keep their partners financially dependent. But people do still escape abuse, even in dire financial circumstances. And if you have children, no abuser can escape paying child support. If the state can find the money, then your partner will pay child support. And the state can find anything but cash paid under the table and stuffed inside a mattress will leave a trail for the state to find, either through bank records, employment records, or taxes. Everything is online now. Almost no one really lives off the grid. If your partner earns money, spends money, and pays taxes, then the state will find that money. Incidentally, a court may not be able to find that money - the court system is still stuck in the 1950s, so don't let a lawyer scare you about hidden funds or anything that's hard to prove in court. The rules are set up so that every parent owes child support based on their gross income. And the state applies a formula to require every parent to pay that support. You can also add your children's expenses to FL Form 130. So basically if you can file a divorce, the state will go after your ex for a minimum level of child support, and your ex will owe you for any expenses that you added to Form 130. Just keep your receipts. So the rules are much easier for parents escaping an abusive situation now than in the past. Don't let your abuser say something like "I'll sit in jail before I'll pay you a dime." That might have worked in the 1990s, but today they'll still owe you even if they're in jail. And the state will collect.