We could do this as follows:
- Populate a "Command Block" with the correct
/docker command to start and/or stop a container
- This block can be activated
- a) With a button (placed on top of it)
- b) With redstone
With the latter, a circuit such as this one can be used to implement something similar to Docker Compose :)

A big benefit in my book is that we can vary container start order by using more inverters