I don't want to talk badly about their father, but I'm extremely worried about my daughters' well-being. How do I explain this to them?
Your daughters aren't little kids. Find out if they want to continue visiting with their dad or if they're scared to do so. Consider whether or not his abuse of his current wife would influence his behavior with your children and whether or not your girls have ever witnessed this abuse. Also, if he receives treatment for any mental disorder he may have, should he be denied unsupervised visits? I'd like you to inform your decisions by considering these issues, not the least of which are your daughters' opinions and desires.