It's all about what you can prove in court. In order to get sole custody, you would need to show that the stepfather is creating an environment that is clearly and convincingly not in the children's best interests. You will need objective evidence of the hostility of the stepfather -- your word against your ex will not be sufficient.
Assuming that you can convince the court that the situation is bad enough to warrant a new custody hearing, then you would probably need to pay for a custody evaluator to interview the children and parents and report to the court on his/her findings. This is expensive, because the evaluator is usually a psychologist and the process requires several home visits. Then, if the evaluator sides with you and other parent disagrees, there will have to be a trial, which will cost even more money.
A highly disputed custody action can run $40-$50,000, when considering the attorney and expert witness fees on both sides of the dispute. So, unless you have some really strong proof going in (like physical injuries after a fight and a police arrest of a parent for domestic violence), your road will be very difficult and expensive, with no guarantee of success.
Contact a local family law attorney and discuss the specific facts.
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