Can you set up a SQL server maintenance plan to restore a database? I am looking to setup a maintenance plan that makes a backup of a database (Database1) and then restores to another database (Database2) to confirm that it is able to restore successfully. 

Can I do this as part of a maintenance plan and have SQL server mail me if it fails either the backup or the restore?
Yes you can. After your backup task, add an Execute TSQL task that has the restore command. Join them together with a success constraint. 

Add a Send Mail task and join it to both the backup task and the restore task. Make it an OR constraint and convert it to a failure constraint rather than success