Sending a text from my computer messed up 3 iPhones

Has this happened to anyone else? Because Apple products are now interconnected, I tried to send a text from my MacBook Pro to my parents in a group message. It didn't work, which wasn't a big deal, but apparently, this was the catalyst for a major problem.

My mom noted that her messages now identified me as "maybe (my name)" in the group message, so she went to change the name of the group. This affected ALL THREE of our phones, changing the name of our group to her preferred setting (my name and my dad's). I didn't want this, so I deleted the group and started a new one. This was a week ago. Today, my mom noticed again that the phone identified me as "maybe (my name)" and went to fix it again, once again changing the group. When I went to fix it, I see that now we are starting multiple new groups every time we go to text each other.

This is driving me INSANE! I've done everything I can think of, and there is no solution I can come up with that fixes this problem. I need the community's help. How do we fix this? Should we bring the phones to the Genius Bar and let them sort it out?