Sounds like a dodgy router. If the WiFi goes down for all devices and WiFi keeps working. I would replace it rather than adding a second router. I like TP-Link for their value, use of external antennae and build quality. Although the setup isn't as user friendly. If you don't understand networking a Linksys/Cisco would be a better choice, from an ease of setup standpoint.
The TP-Link Archer C1200 is by top choice for what you get for your money.
https://www.amazon.com/TP-Link-Gigabit-Wireless-Archer-C1200/dp/B01IUDUJE0/ref=sr_1_7?ie=UTF8&qid=1483377552&sr=8-7&keywords=tp-link+router
If your computer is far away from the router. A second router setup to act as an access point. Would be great for boosting your WiFi range. Just turn off DHCP on the secondary and give both the exact same wireless settings. Then your devices will automatically connect to the strongest signal. Be sure to give the second a static IP address so you can find it to change settings.
For secondary settings
If your primary has network settings such as
IP Address: 192.168.1.1
Subnet: 255.255.255.0
DHCP Server: 192.168.1.100 to 192.168.1.200
SSID: My Home Wireless
Key: Password1
Encryptions: WPA2 AES
Your secondary router should have a static IP setup as
IP Address: 192.168.1.2 (or some other unassigned address outside the DHCP pool)
Subnet: 255.255.255.0
DNS: 192.168.1.1 (or your ISP DNS or DNS server of your choice like a Google DNS)
Gateway (router address): 192.168.1.1
DHCP Server: disabled
SSID: My Home Wireless
Key: Password1
Encryptions: WPA2 AES