Unfortunately I can't see the screenshots (probably blocked by firewall), but I have installed multiple versions of SQL Server side by side without an issue.
It should be no problem to install SSMS 2008R2 and SSMS 2012 on the same machine.
You only need one though, you can manage SQL Server 2008R2 perfectly with SSMS 2012.
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My blog at https://sqlkover.com.
MCSE Business Intelligence - Microsoft Data Platform MVP