server 2008R2 Domain Controller upgrade to 2012R2 Domain Controller

Log into the 2008R2 server and put in the 2016 DVD. When setup starts it will come to a decision screen and select upgrade, leaving everything intact.  It should keep all your apps, configurations and settings.

I wouldn't  besides the fact that a DC should never run hyper-v or RDS, that those coexist will probably make the upgrade hell. Use this opportunity to migrate to new clean installs /VMs.

No  but when an opportunity presents itself to fix a blatant bad configuration, it should be taken. Intentionally moving forward with a bad configuration isn't acceptable either. If I were a new hire and found that the domain admin password was 'password' I wouldn't simply say 'oh well  that's the way it is, and what I was dealt.'  That becomes a priority change. This isn't far from that scenario.

I agree fully, but you also have to take into account changing an Admin password is easy.  Financing new equipment and moving major functionality can be a little bit harder and could be totally of the hands of IT.

Existing equipment is already running hyper-v and RDS  considering the light overhead of a hyper-v hoist and the 1+x licensing of windows, this should be a zero cost change as far as hardware and software. If the server really can't handle splitting those roles out  it shouldn't be running them together anyways. That close to the edge would cause the DC to be non-responsive every time RDS usage spiked  resulting in system outages.  So cost is not a factor in such a change.