OpAmp question

Got a weird one for you all. I have an opamp that seemingly refuses to output a voltage in unity gain mode.

The circuit is below. Its based on two Sparkfun LMV358 boards where I have reconfigured them to be unity gain.

The use case is that I need a very clean 1mV (and below) sine wave. The function generators we have are noisy if you ask for 1mV output. This circuit should be taking in a 2v p-p sine wave and attenuating it down to 15mV p-p. So the signal is attenuated and importantly so is any noise on the output of the function generator. So I can vary the 2v signal and get very very precise changes in the 15mV output. This means I can drop the input singal down to say 300mV and then get a very very clean 1mV sine wave.

However I dont seem to get anything out of the second opamp stage. If I disconnect the +ve input from the resistor divider and connect it to the input then I get a nice copy of the input sine wave. So opamp is working fine. But if I feed in the 15mV I get nothing on the output,

Am I right in thinking that as I am asking the opamp to buffer 15mV in unity gain, that the opamp cannot do this due to it NOT being a rail to rail input opamp?

If thats the case, would https://www.ti.com/product/TLV9002 be a drop in replacement as I can take off the LMV358’s and replace them with the TLV9002 as both are SOIC8.

Thanks in advance!

The use case is that I need a very clean 1mV (and below) sine wave.

Just use a voltage divider. The op amps will add noise to the signal.

The use case is that I need a very clean 1mV (and below) sine wave.

Just use a voltage divider to attenuate the signal.

The op amps will add noise.