Simple answer: use a live system.
If another partition has been mounted on your root's
/home, indeed you cannot simply unmount it, or even re-bind the mount. However, a live system has it's own /home/ arranged for and doesn't use the partition that normally provides your root filesystem. So on the live system, simply mount your root filesystem and you can access the original /home directory from there.
Finding a live system shouldn't be difficult, because there are quite a few distributions that provide a live CD image that you can burn on CD, or put on a USB drive to boot from there. Some of the distributions that offer this are Debian, Knoppix and MX Linux.