How to separate peanut oil from roasted peanuts at home?
Disclaimer: I did not try it, but it should work from a chemical point of view.

Put the ground peanuts or peanut butter into a pot and add the same amount of water*, stir well and bring to a boil. 
Pour it in a Fat Separator to separate oil and peanuts. Pour the peanut water mix into a heat resistant form and put in the oven to dry at low temperature.

If you want to use the peanuts minus oil for baking you could use milk instead of water, that way you don't have to dry it after separation.

*if the mixture is too thick for the fat separator use more water.

As an alternative you can use the method used when making paneer or potato dumplings: Put the ground peanuts or peanut butter in a dry cloth. Take the four corners together and spin to squeeze oil out. This is much easier but less efficient as well.