Your issue is with 'double-hop' authentication. When you're logged onto Server1,you are able to authenticate directly to Server2, but when you are connected to Server1 via your PC (using your Windows credentials), in order to connect to Server2, Server1 needs to be authorised to delegate(forward) your credentials on to Server 2.

If you do a search in BOL, for 'double hop' you should find everything you need to get this up and running (with a little help from a friendly Domain Admin:-)). Pop back if you're still struggling.