Issues with SMS between an iPhone and Android

I have an iPhone and I'm having a persistent issue sending direct SMS messages to Android devices. I've had multiple phones (and multiple SIM cards) and the issue still occurs. When I send an SMS message to an Android, it shows up as sent, but the receiver does not receive it. This happens when message(s) are sent to a singular Android device and a group of Android devices. I can receive messages from Android devices, but if I try to respond, the receivers report that they do not receive the reply. The only time an Android actually receives my message is if it's a group message to multiple people and there's an iPhone included in the group. I've spent countless hours on the phone with AT&T support and they have not had any solutions. Has anyone else had this issues? And/or does anyone have any innovative solutions?