Group chat/messaging with email alerts

Hi, I am trying to find a good plugin for WordPress that will allow my church to have a place for members to chat or share information that uses an email list type format. We have been using HostGator’s Mailman list and it is great, but the HostGator mail servers are so often blacklisted, that most users don’t get messages. I need something where I can set members up, add their email addresses, then when anyone has something to share all members in the system get the message and can reply back and forth without having to be logged into WP. It also needs to be safe and secure. I know it is a lot but any suggestions?