I am trying to create docker image with alpine linux, which after run will create container with 2 running programs. This 2 (in my opinion - I don\'t know docker well) can\'
You would need to run the first program in background for the second line of your script to execute.
Whenever you have two processes which must run inside one container, there is the risk of zombie processes (ie the container won't pass correctly the SIGKILL signal to all processes).
Use as your base image phusion/baseimage-docker: it is made for managing multiple processes.