I have an original iPhone SE. I've never had any issues with it with sending iMessages or SMS, but I paused my service for a month or so last fall because I was out of the country. When I came back and re-activated service, I could no longer send SMS to groups. I can send them individually, if it's only text, and there are no pictures or video involved, in which case that doesn't work either. I have spent hours on the phone with my carrier and even switched carriers, but still have the same problem.
Thank you for using Apple Support Communities! We understand that you need help with group messages on your iPhone SE. We are happy to help out. Check out the following support article under the section titled "If you have issues with a group message", which provides some troubleshooting steps to try for this behavior: If you can't send or receive messages on your iPhone, iPad, or iPod touch
I've tried those options, but the issue persists.
Thanks for reaching back out and letting us know. At that time, we recommend reaching out to Apple Support here for further support: Get Support