You should not draw a significant amount of power from the Arduino 5V pin. The pin is intended only for things like low power sensors, or a couple of LEDs.
What relay module do you actually have? Some have on board transistor drivers, and some don't. If yours doesn't, there are lots of relay driver circuits online, you can just Google them. Even just find a relay module schematic, lots of those online too.
@jremington just reminded me, the relay control input drive is not the only problem. But if your module has no transistor, driving it from an Arduino pin isn't okay, either.
The 5V output can supply more current, or at least supply it more safely, when the Arduino is powered from the USB connector. Barrel jack powering is the worst. But as a benefit, you discovered the weakness...
I have a Uno (Official product) and a 4-relay board.
I am using 9V via the barrel jack.
I am click-clacking one relay, its output is running an LED like the OP's.
Uno 5V measures 5V when the relay is actuated and when it's not.
The switched output via the relay measures 5V, too.
I can make a vimeo if necessary.
Which Arduino (I have learned not to trust Fritzing pictures).
How do you power that Arduino.
You mention 9volt.
Smoke alarm battery?
That will struggle to provide the current for an Uno + relay (125mA), and could cause VCC to drop.
Which sensor. I don't see one on that toddler drawing.
Leo..