The underlying error appears to be an issue connecting across the network to the other server. From the server that you are running the SSIS instance from it seems like it is unable to connect to the remote SQL Server perhaps because of firewall or other issues, or perhaps the server is on another network and there isn't a trust across the domains.
To debug this I would first start by testing that, from the SSIS server, you can successfully connect to the remote SQL server. Note that you should be using the credentials that SSIS will be using. If the connection fails then it is a credentials/network issue. Given the 2 errors you posted that is where the problem seems to be at.
To test you can use either SSMS on the SSIS server, if it is installed, or create a simple Powershell script to connect using SQL client.