If I run two mysql containers, it won't necessarily take twice the resources of a single mysql containers
It's complicated, but essentially, no.
Docker images, are built in layers. Each layer is a step in the build process. Layers that are identical, are shared between containers to the point of it taking up the ram of only running the layer once.
Although, it should be noted that docker doesn't load the whole container into memory, like a normal linux os. Unused stuff will just sit on your disk, just like normal. So rather, binaries or libraries loaded twice via two docker containers will only use up the ram of one instance. This is similar to how shared libraries reduce ram usage.
Docker only has these features, deduplication, if you are using overlayfs or aufs, but I think overlayfs is the default.
Should you run more than one database container? Well I dunno how mysql scales. If there is performance benefit from having only one mysqld instance, then it's probably worth it. Like, if mysql uses up that much ram regardless of what databases you have loaded in a way that can't be deduplicated, then you'd definitely see a benefit from a single container.
What if your services need different database versions, or even software? Then different database containers is probably better.