Hi Jessey,
Well, now that you have a stable reference, I think the problem might be in using 2 different regulators.
The MIC2954-03BZ is a 1% LDO part, and the 7805 will only hold to 4% of the target voltage. I usually see them running at around 4.85 - 4.90V.
Since the "CMOS circuit" is powered from VDD, any change in the voltage may be changing the "Analog Out" value as well, causing it to act as a "Ratiometric" sensor. So even with a stable ref., the readings will still change according to the supply voltage.
I think you might be able to get rid of the 7805, and still have the relay select the power source to the MIC2954. Something like this.
<img src="http://www.picbasic.co.uk/forum/attachment.php?attachmentid=422">
Added: The other half of the voltage divider going to RC5 (for AC power detect ??) is 1K. I cut the picture off a little short.
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