You can restore the .trn files using RESTORE LOG (WITH NORECOVERY).
You need to do a full backup & restore (WITH NORECOVERY) of the database before you can restore any transaction logs.
If you can setup a VPN, it's best to let SQLServer do the whole backup & restore & verify - the copy phase is pretty easy to override - just write your own copy SQLAgent job & disable the copy job that SQL setup for you.