The short answer is -- maybe. It all depends on the facts of the case, what is going on with the other spouse, your support groups, and the like.
It may not be an easy fight, and you would have to be prepared to have your past brought out and argued about in court. The divorce could get very ugly, and expensive, possibly requiring a custody evaluation to fully address any safety concerns.
The best thing to do is find a good attorney, one who has access to child-custody experts, and be the moving party. In my opinion, it is always better to be presenting facts, even not-so-good facts, first, rather than having to answer claims of bad behavior and then defend against those claims. Steal the opponent's thunder by admitting the problems first, and present the curative facts to show the problems are addressed.
Answered on Jun 10th, 2015 at 7:19 AM