How can I control an IR jammer or other device remotely?
You may use any type of RF to control this. Arduino has a lot of material on this, or you can for example use a Bluetooth Low Energy Smart Beacon Kit for the hardware (modify its firmware) and control this with your android/iphone with Nordic Semiconductors already ready to use apps. I recommend the nRF UART app on Android since you can customize it to send whatever you want. 

You want to connect one of the GPIO's of such a kit to the button of the IR jammer (remove said button, connect your GPIO to the input of the microcontroller within the kit and connect their grounds together) and you will be able to "push the button" from your cell phone. 

There are also a lot of Arduino shields you can use, e.g. a WiFi shield, whereas you connect it the same way but you'll be able to activate the jammer from a website.