As you go through your divorce, you and your spouse will transition from being wedded partners to a relationship that is focused on your roles as co-parents. You'll still be in each other's lives for many years -- even when your kids become adults.
This doesn't necessarily mean that your relationship will get significantly easier -- at least not at first. You'll still be the same people you were when you were married. If you had trouble communicating civilly, that's not likely to change overnight. Anger and resentment over each other's actions may continue for a while. However, you have to commit to putting the past behind you to focus on doing what's best for your children.
If communication issues plagued your relationship before your divorce, they aren't going to suddenly disappear as you begin co-parenting across two homes. If your spouse wasn't a good listener or you expected them to know what you wanted rather than telling them directly, those bad communication patterns aren't going to change unless you recognize them and commit to changing them in order to be the best possible co-parents.
That commitment to good co-parenting also means putting anger, hurt and resentment about past actions aside. That takes work -- and maybe some therapy. You may need to keep your communication completely child-centered to avoid rehashing old grudges and reopening old wounds.
It's essential to recognize that even if your co-parent was a "bad" spouse, that doesn't make them a bad parent. Even if their parenting style is different from yours, they love your kids too. Unless a parent is truly abusive or neglectful, kids are typically better off when they have both parents in their lives. Parents should support their kids' relationship with their co-parent and not try to undermine it by badmouthing their parent to them or around them.
If it's still difficult to communicate civilly with your co-parent, you may be better off limiting direct communication. Co-parenting apps help parents stay current on what's going on with their kids without having to talk to or even text or email their ex. Having a detailed, well-drafted parenting plan in place can also minimize the need for communication. It can also clarify expectations and minimize confusion around custody exchanges and other matters. All of this can make the transition from battling spouses to amicable co-parents smoother.