https://support.apple.com/en-us/HT204833
I have been having trouble for several months now trying to use Digital Touch messaging between two Apple watches on the same Apple account. I'm not alone. Many families have had the same trouble and it seems Apple tech support is at a loss to either understand the problem or believe there is no fix.
In a case where two Apple watch owners are on the same account, the secondary family member may be able to send a Digital Touch message to the primary account holder but not the other way around. If the primary account holder tries to send a DT message, what happens is the little drawing is sent out and within seconds echos back to the sender's watch and never shows up on the intended destination watch. But if the secondary person tries to send the DT drawing, it goes through without trouble. At least that was in my case. In other cases people have complained the opposite.
The problem lies in the way one sets up iMessaging addressing. It would seem logical to list the watch owner's email address as well as the iphone number in the watch setup so that imessage can be sent to an email address the same as most people do with text messaging using a phone number. But with iMessage and DT use this is not possible. To prevent DT from getting confused, only the watch owner's phone number should be listed by all family members. Then to receive an iMessage you must send it to the recipient's phone number only. In the settup for imessage uncheck any email addresses. Leave only the phone number checked. Once this is done on all phones, DT alerts will automatically appear almost instantly on the recipient's watch.
In addition if you have old message threads in your history, you will need to delete these from all phones. Sorry about that, but if that history is present in your account, it will access the email and prevent the recipient's phone number from being used and the DT will not be sent.
The rest of the setup for DT also must be done such as only Apple Watch owners,
who are in your Favorites can receive your DT message. If they are not in your favorites, and have an Apple watch, then there is no way for you to send or receive a DT message from them.