Do put the kids first.
Other than the kids, it is now a business negotiation. Do get a lawyer, don't rely on goodwill of the other party.
Do try to mediate as much as you can. It is cheaper, faster, easier, and you have more control over the outcome.
Don't do anything rash or stupid. As much as you may want to, do not denigrate the other party to anyone, especially the children or any extended family.
Don't expect the court to care about who was right or wrong or guilty or good. All the court will care about is that the kids are given the best situation possible and that the two of you agree to the property division, which will probably be very close to 50/50 even if the other party is an axe murderer.
Do keep the recent inheritance separate; do not comingle or retitle those assets in any way.
Do realize that you don't have to split each individual account or asset 50/50 - as long as the total is 50/50 then the court should be fine with it.
In my state they only care until the kid graduates from high school. Beyond that, the higher earner should expect to pay child support for the middle school child. Be aware that each state has child support guidelines that are formulaic - even if the other party wants/needs/expects more, the formula amount is presumed to be correct.
Even though *my* advice is accurate, don't trust what you read on the Internet. Only trust the law in your state and your attorney.