How can I use applicaitonimpersonate role on a on-premise application to update calendars in Office 365?

We are in the process of moving to Office 365, currently have Exchange 2013 servers on-premise.
We have an on-premise application that uses the applicationimpersonate role to update user's calendars.
We want to be able to use this same on premise application when we move our mail boxes to O365.
We will retain an on premise Exchange server to relay SMTP email from local servers to O365 mail boxes.

We currently are testing with a MS O365 trial. I have set up an admin role for applicationimpersonate and added a member to this role in O365.
Below is what I put in for the Exchange/impersonation information in my application web.config:

  <add key="ExchangeServerUrl" value="https://onpremise servername/ews/exchange.asmx" />
  <add key="ExchangeServerUserId" value="O365Account name"/>
  <add key="ExchangeServerPassword" value="PW"/>

We are getting 401:Unauthorized message back  from the EWS.

I believe we need to set up a domain/forest trust between our on premise and the O365 environment but not sure.

Any suggestions on what we need to get this applicationimpersonate role to work with our on premise application and O365 will be greatly appreciated.

Thank you,