Why does the drone's remote control interfere with the image transmission system
Most of all, this is because your image transmission system has a cheap radio receiver which has low dynamic range, so strong signal from remote control affects it's reception. It is also possible that your remote control uses cheap radio transmitter, which has out of band emission which falls into image transmission system band.
You can check what is the root of cause with spectrum analyzer. If there is unwanted emission from remote control on band of image transmission system, then this is due to low quality transmitter of your remote control.
But I bet this is due to low quality radio receiver (low dynamic range) in your image transmission system. This is because it's hard to build cheap and compact receiver with high dynamic range. You can try to fix it by using high directivity antennas for remote control and for video placed at some distance from each other in such way to avoid direct reception of remote control signal on video receiver antenna.