Use router as Wifi Source? (noob question)

I have my cable modem plugged into a router. The router is then plugged into two macs via ethernet. It works great but the wifi is terrible, even when right next to it. Its even worse when I want to use it in the living room (the main room I would use mobile).

My question is this:
Can I route a third ethernet cable from my router to an additional second router in my living room; this second router would be used soley for a strong wifi signal. Kind of like an extender, but hardwired to my original router.

I don't want to spend money on a new router to replace my old one, and my dad has a router I can use for free to use as this "extender".
Is this a good idea or will this mess something up with my original router, etc....

 

Hallux

thats a good point but I do have reasons behind not replacing the router.

1. The router works great for sharing files between the macs. My last router didn't.
2. My dads router is a cheaper model
3. I had to have someone configure my router customized to work with a few different complicated things I didn't understand. like accessories and programs.
4. I already have an ethernet cable wired into the living room that is available to plug in at any time. (Used to use on Roku, but unused now).
5. I would be using the wifi in the living room and not in the room on the other end of the apartment (where current router setup is).

phew... anyways you can see how just plugging in the extra router seems like the LESS complicated option

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hmm I will look into this bridge mode...