Using differential Amplifier on LTC1968, and the input voltage changes; please help

Hi Shurp:  Yes, this happens simply because the LTC1966/7/8 output is not buffered.  The data sheet spec for output impedance of LTC1968 is 12.5k Ohms typically.   So you need to buffer the outputs before doing the difference amplifier.  Or, you could use a much higher impedance difference amplifier (such as LT1991), except that the + and - inputs of a difference amplifier present different loads upstream.  The +input presents 2R to ground, while the -input presents 1R to +input.

GlenBrisebois Per your recommendation, I used LT1991, and I increased the gain until the input was not affected. Below is the diagram I chose to use; the diagram below is on Page 19 of the datasheet. The issue I currently have is that the output is not stable. Even after using a 1uF capacitor on the output, there is about 10mV fluctuation, measured by a microcontroller (Arduino nano). Just to reiterate, the input to the LT1991 are signals from LTC1968 which seems stable. Not sure why the output of LT1991 fluctuate. I hope to hear your thoughts on this.

LT1991:https://www.analog.com/media/en/technical-documentation/data-sheets/1991fh.pdf

GlenBrisebois Per your recommendation, I used LT1991, and I increased the gain until the input was not affected. Below is the diagram I chose to use; the diagram below is on Page 19 of the datasheet. The issue I currently have is that the output is not stable. Even after using a 1uF capacitor on the output, there is about 10mV fluctuation, measured by a microcontroller (Arduino nano). Just to reiterate, the input to the LT1991 are signals from LTC1968 which seems stable. Not sure why the output of LT1991 fluctuate. I hope to hear your thoughts on this.

LT1991:https://www.analog.com/media/en/technical-documentation/data-sheets/1991fh.pdf