I am facing issues with statistical analysis.

My statistical analysis shows a significant relationship between the S & P 500 index (DV) and the US inflation rate (controlled variable) but when I add the US real GDP growth rate as a controlled variable with inflation. It shows an insignificant relationship between inflation and the S & P 500 index.

Is it mandator to use both as controlled variables?

Can I skip either inflation or GDP growth?

I would be highly obliged for the kind input.