Father and Son have different idiology. What 's the role of a Mother, who wants peace in the family?

Talk to both of them together and let them know that they can have their ideologies without trying to force it on each other. People with different view points can co-exist. It's called diversity, and it is a sign of maturity.

Tell them that your ideology is 'Peace in the house' and if someone tries to challenge that then you will knock their head off.

Step aside - I lived in this family and my mother was always interceding. It didn't work. They will either learn to live with each other and respect one another's opinions or they won't. But whatever the case is you will not be able to end the conflict. The stress between fathers and sons is eternal - literature and history are replete with this problem and its' many and varied outcomes. "Oh Absalom, my son my son" , is just one example. So just bite you lip as often as you can, and when it gets unbearable remind them what misery they cause for everyone. Make them realize that the stress they create is owned by them both.

try to melt the two ideas together. like republican and democrat the middle ground is independent

also try telling the mature father that his ideas are what you like but that today at schools and all different things are being preached so let him talk and he will evaluate himself. people frequently answer their own questions if they are allowed to talk them over. when my sons talked I would get hot and my wife would say listen please. then I would give them examples. debate must show examples. kids want to see proof. ideas are not proof.

Steer conversations away from their differences and find topics they can agree on. They have to be mature enough to be civil to each other and agree to disagree.

You should stay out of it! tell them keep there political believe to them-self.