voltage divider and running other circuits causes different voltage readings

You are using a 10R and a 20K resistor for your voltage divider. This is incorrect, take a look at Wawa's code: use 6.8K and 100K respectively. And you didn't use "analogReference(INTERNAL);" in your setup.

Also, you are using external pull-down resistors for your buttons, that's completely unnecessary: all Arduino's have built-in pull-up resistors. Read more on how to take input from a button here.