Connecting ADC pin to op. amp. output distorts signal
A few things to make sure of:


Make sure you have decoupling capacitors (e.g. 100nF) on all opamp power pins.
As a unity gain configuration is sensitive to capacitive load (the ADC input pin), try isolating it using a series resistor (between opamp output and ADC input), value say between 220&Omega; and 820&Omega;.
Make completely sure there is nothing else affecting the ADC input, and it is set correctly as an analog input - check it with a known source such as a signal generator to confirm the same does not happen.
Make sure the analog section and the uC share a common ground.
Check none of the opamps are oscillating at any point.
Check supply rails are okay (check under load also)  


Let us know how it goes, it should be a reasonably easy issue to track down, but no doubt Murphy will have something to say about that ;-)
A proper schematic with all parts present would be helpful (i.e. I'm assuming the opamps have decoupling caps but you did not include them on the LTSpice schematic)