What is the safest way to run SSIS on Multiple Named SQL Server Instances? I have an Active/Active SQL Server 2008 R2 cluster. There are two named instances on each node and no default instance. 

I need to deploy SSIS packages to the different instances. To do this, I needed to modify the  MsDtsSrvr.ini.xml file to add the instance names so they would be seen by BIDS and SSMS. I put all 4 instance names in that XML file (on both nodes) and restarted SSIS on both nodes. I can now see the folder for each instance when connecting to any instance in SSMS through an Integration Services connection. However, clicking the 2 instance names that are on the other node generates a login failure since they are not active on the current node. Maybe this is just an inconvenience, but am I going to run into any issues with this setup? Or is there a way to do it that makes more sense?
I dont see anything wrong in your setup. To be fair, this is the correct way of setting up SSIS in a clustered environment.

Read up SSIS and clustering: What you should do instead

Also for the login failure, its worth to check  the Windows Server 2008 R2's firewall rules  to allow an inbound rule for either the msdtssrvr.exe executable or the DCOM port SSIS listens on.