Apparently Amazon SNS will not do mobile-to-mobile push.
Reply from Amazon:
To answer your question, no AWS SNS will not send a direct push message from one mobile device to another. SNS uses Amazon's servers as the publisher which will send the messages to the subscriber end points. You can view more of this here:
http://docs.aws.amazon.com/sns/latest/dg/SNSMobilePush.html
You would need to use the application on the mobile device to handle the messages from one device to another using the Google Cloud Messaging (GCM)
Answer link: https://forums.aws.amazon.com/thread.jspa?threadID=144057