I want to build an outlet that I can control on a timer or through a device like a smartphone. I am planning on using a solid state relay for this job. I'm aware of the electrical code stipulation that all low voltage and high voltage wires must be separated by a permanent barrier, as explained in this question. I was going to use a double gang box from home depot like this one to accomplish this. My question is, with the separator there, how do I connect the relay to the low voltage control?
You can mix Class 2 conductors with power conductors in boxes if the power circuit conductors are introduced solely to connect to the equipment connected to the Class 2 circuit.
Class 2 circuits voltage and current limits are well-defined by National Electrical Code (NEC.) Also, NEC defines spacing between the class 2 conductors and power inductors.
See NEC article 725 for more.