Welcome to the Apple Support Communities! I understand you are having issues sending picture messages with iMessage on your iPad. It sounds like you have done some great troubleshooting already by resetting and turning iMessage off and back on. I would suggest the steps in the following article under the If you can’t send and receive iMessages section.
If you can't send and receive iMessages
You will need these to send and receive iMessages:
- An iPhone, iPad, or iPod touch
- iOS 5.0 or later
- A cellular data connection or a Wi-Fi connection
- A phone number or Apple ID registered with iMessage in Settings > Messages
To resolve issues with sending and receiving iMessages, follow these steps
- Check iMessage system status for current service issues.
- Go to Settings > Messages > Send & Receive and make sure that you registered iMessage with your phone number or Apple ID and that you selected iMessage for use. If the phone number or Apple ID isn't available for use, troubleshoot iMessage registration.
- Open Safari and navigate to www.apple.com to verify data connectivity. If a data connection isn't available, troubleshoot cellular data or a Wi-Fi connection.
- iMessage over cellular data might not be available while you're on a call. Only 3G and faster GSM networks support simultaneous data and voice calls. Learn which network your phone supports. If your network doesn't support simultaneous data and voice calls, go to Settings > Wi-Fi and turn Wi-Fi on to use iMessage while you're on a call.
- Restart your device.
- Tap Settings > General > Reset > Reset Network Settings on your iPhone.
If the issue continues after the initial 6 steps be sure to continue with the next 5 steps under the If you still can’t send or receive an iMessage, follow these steps section.
I hope this helps,