Hugs! I got divorced a year after I get diagnosed with BiPolar I. We ended up being 60/40 custody (I had the 60%) before my ex-husband moved out of state.
In my experience, I had to show the court that I was competent to be a parent and my psychiatrist was willing to provide medical testimony regarding my mental state. I had a very good lawyer who was able squash my ex-husband from bringing it up to the judge.
Without knowing what state you live in, it's tough to say if there is anything that would cause either one of you to lose custody.
In the state of Missouri, a guardian ad litem (GAL) would be appointed by the court to represent your children if there was a significant custody dispute regarding the kids (e.g., one parent wants to have full custody and the other parent disagrees). The GAL would do an interview (sometimes more than one) with your kids at school to get more insight into their life, and they would have separate interviews with the parents.
Facebook has a lot of great divorced parent support groups: Divorced Parents Unleashed and Divorce 101. There are a lot of other parents who can guide you through the steps you need to take in the early stages of divorce.
I hope this helps- I don't want to overwhelm you with information but let me know if you have any questions.
I am two years post divorce and I feel very relieved that it happened. Originally, I did not want the divorce at all. I am 100% confident that I have done a better job handling my Bipolar symptoms as a single mom vs being locked in an unhappy marriage.