You need one router + additional access point using wired backplane. Repeaters in mesh mode will suck with bad connectivity - you need to add more of them so they have overlapping good coverage.

If you extend with wired connection you will have much better performance.

The question is if you want smart client offloading so when you walk around the house the APs are trying to be smart about passing over the clients to the stronger signal, then you need something that is a bit smarter (look into unifi for example). If you dont care about it that much then it doesnt matter, you can repurpose what you call a "router" and just run it in wifi ap mode. Also make sure you only configure dhcp forwarding on the second one otherwise you will have local connectivity issues