Usually you have to install SME on all DAG members and make sure the SME Service is able to communicate through the windows firewall if not disabled at all. the sme service will crash if you connect to the service without firewall exception or disabled firewall, you have to start the service again after that.
Also check the permissions of the Service account the snapmanager is running under - i'm not quite sure about the error message but it seems the same error if the service account is _NOT_ Local administrator on all DAG members.
Firewall and Service is likely the issue here. Make sure the SME service is running with the appropriate acct/password. Also ensure the Microsoft Information and Replication service is also running on all the nodes.
I have a 4 node DAG - 2 in Peoduction, 2 in DR. One of the DR nodes is a lagged copy.
I ran Exchange SP2 on each box with intermittent results on each box. Sometime I had to try 3 or 4 times to get the install done. I think the lagged copy server has suffered from a partial upgrade of SP2 which has affected the Exchange install. The SA service won't start. I removed the lagged DB copies from the DAG then removed that server and I don't get the issues I was having previously with SME.
I do however have an issue with trying to schedule a backup across the nodes now with many errors appearing when atetmpting to create a task