There are a lot of variables. Has your ex seen your child at all in the last five years? If so, how often has he seen your child? Was he required to complete a 52 week program for DV, and if so, did he? The law does not make you unfit simply because you have cancer. If the court finds that your ex has worked on his behavior, and is a capable parent it may modify custody in some form, but without more information it is hard to know. The problem is I don't know all of the facts.
You should contact someone in your area who knows your local rules, the mediators, and the judges. I would not go this alone, it is difficult to undo a bad decision, and you don't want to make any mistakes. If you can't afford to hire an attorney for the entire process, you should at lease seek advice from a local attorney before you do anything.
Cancer is not a basis for a change in custody. Additionally, if there was prior domestic violence the abuser would have to show a completion of 52 week program or a rehabilitation of that problem for the court to change custody. If your ex has no other basis other than presenting that you have Cancer, I think it is unlikely a court will modify custody.
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