I'm going to turn on a secondary router when my dad turns off the main one at 10pm
Why run a second router?
Because I feel uneasy in my house when he turns it off.
Try telling your father that you're uncomfortable with the first router being turned off. That way he might be willing to just leave it on.
Why would I do that? He's not a part of my life.
If he controls your router than he is part of your life. Having a router stay on all night isn't a big deal. Try talking to him and maybe you can convince him of this so you can avoid the hassle of using a second one.