https://www.ti.com/lit/ds/symlink/ina118.pdf
what is the time base on your scope shot?
20mS
Where is this resistor, is it somewhere in a switching power supply?
After a H Bridge.
Was the scope shot done with a neatly terminated bit of x1 coax, or with a scope probe with its gnd lead dangling all over the place.?
...with a scope probe with its gnd lead connected to GND.
What is the pcb layout like….are all the signal traces routed in diff pair style?..low as possible loop area?
As I had to change the first circuit of sensing current, the connection between shunt resistor and INA118 is through a twisted pair and not in the same board.
Have you got an RC filter across the sense resistor?
No.
If you remove the probe from the resistor, do you still see all that noise? (with the scope lead in roughly the same physical place)