I had this same exact problem.
I fixed it by turning off iMessage in the iPhone that received the sketches but didn't sent them. First I unchecked every email address that iMessage could use, leaving only the pone number able to send iMessages.
Turn iMessage on again and verify that the phone number is the only one that can send and receive iMessages.
Delete the prior conversation with the recipient in the iPhone that couldn't send sketches.
Send a couple of iMessages from the iPhone that could't send sketches. Ask for the recipient to answer a message.
It should work now. Both Apple Watches should be able to send sketches.