Hello, short answer: if possible you could try moving the router as close as possible to your external walls, and then if you have power in your outbuilding, add the wifi extender there. You can also try different combinations to see which location works best for you.
Ultimately, you've got 4 main ways of boosting your Wifi signal.
Wireless access points use multiple radio signal transmitters and receivers to give your network's signal a boost. They use MIMO, or multiple in and multiple out, technology along with reflection and amplification of radio waves to cover a much larger area than a standard router. Access points require a power supply and Ethernet connection.
Internal Boosters and Add-on Antennas
Internal boosters use the same MIMO technology as access points to boost reception. Router antennas can be screwed off and replaced with high gain antennas to boost the router's frequency range and reception. Antennas may be manipulated to open up the most unobstructed path--it works by line of sight--between the router and the computer's wireless card.
Power-line signal extenders sends data between your computers and modem through your existing house electrical lines. Power-line models pass data between two extenders--one near the modem and one in a remote location. Power-line models use Ethernet, USB and Wi-Fi to communicate with your network's existing components, and electrical pulses to communicate between extenders. Data transferred over electrical lines travels faster than data sent via Wi-Fi. However, these devices are susceptible to interference from other devices plugged into the circuit.
Relays, or repeaters, receive radio waves from your router and "relay" them to give the signals an expanded range. The units contain an internal amplifier that simply receives the signal, strengthens it and passes it along. The practicality of these devices saves on wiring or additional modems.