Mounting cgroups inside a docker container
The conclusion that I came to was that there is no current solution for this since Docker does not support cgroup virtualization nor does the Linux kernel. We need some form of cgroup virtualization in order to implement cgroups inside a container.
lxc does this using a FUSE based solution called lxcfs : https://linuxcontainers.org/lxcfs/introduction/
Also, there is a kernel patch that supports cgroup namespaces which as far as I can see have not been approved : https://lwn.net/Articles/605903/.