Our provincial eventing association created a WhatsApp group to communicate with members. It’s not a group chat - members can’t respond, they can only view information that’s been sent by a group admin.
I had never been a WhatsApp user but I did download it and only use it for this group, plus one person who has a US cell number that would cost $ for me to text (I’m in Canada) 
I’m not sure how tech-savvy your group members are but this did not take any deep IT knowledge to join. The association even had a QR code that could be scanned to join directly, or just search in the app.
Doing this would mean no issues with membership changes because users could remove themselves if they wanted (although they would still need to add themselves).
I don’t think you’re going to find any application that handles everything perfectly - you’ll always have people who don’t check email, or don’t want to download anything, or don’t check their junk mail, etc. If you share info via a couple different methods then your users can decide how they want to receive it. For example: post on your group FB page, send an email, send via WhatsApp group. Let everyone know what methods you’re using for communication and they can choose.
There are companies who can help with text notifications, etc but not sure how big your association is and if you want to pay for it.