I have two Raspberry Pis, one that is a wireless repeater, and another one that I just want to be connected through ethernet to the repeater and be connected. Is this possible to do?
Yes, it is possible to connect your RasPi to a second RasPi working as wireless repeater (access point). Just connect them with an ethernet cable. The wireless repeater must have routing enabled to forward traffic to its uplink. You can also bridge the ethernet interface with the local wireless network (not the uplink wireless connection). Here is a diagram as example to better understand what I mean:
(dhcp) bridge ╱ wifi ┌──────┐ mobile-phone <~.~.~.~.> │(ap0) │ wifi wan │ br0│RPi(wlan0) <.~.~.~.~.> router <───> INTERNET RasPi <────────> |(eth0)│╲ ╲ ╱ ╲ wired └──────┘╱ (dhcp) 192.168.10.1 (dhcp) 192.168.4.1 └─────────────────┘ wireless repeater
The bridge is optional, not necessary needed.