Okay, lets be honest from the start the TG1682G is junk. It should be set to bridge mode and your router should be doing everything else. Hopefully you have a decent router that has better wireless capabilities than the TG1682G. On that note what router do you have? Can't diagnose this with limited information about your hardware setup. Need to include brand name, model and what you use each device for.
Run a traceroute to youtube.com using the following command prompt:
tracert youtube.com
Post the results here.
I have a TP-Link AC1200 Dual Band Router.
Results of the tracert:
Tracing route to youtube.com [172.217.15.78]
over a maximum of 30 hops:
1 2 ms 2 ms 2 ms 192.168.0.1
2 29 ms 14 ms 13 ms 10.14.128.1
3 14 ms 21 ms 13 ms 100.127.41.146
4 15 ms 17 ms 14 ms 100.120.124.20
5 24 ms 36 ms 61 ms ashbbprj01-ae2.rd.as.cox.net [68.1.0.242]
6 24 ms 138 ms 75 ms 98.182.1.86
7 82 ms 1380 ms 135 ms 108.170.246.33
8 143 ms 102 ms 218 ms 74.125.252.39
9 955 ms 155 ms 306 ms iad23s63-in-f14.1e100.net [172.217.15.78]
Trace complete.
Probably an issue with your modem then. Based on how good your router is compared to what the modem provides I would have set the modem to bridge mode and used the wireless router for everything else.
Anyways, get with Cox and see if you can swap out your current modem for an Arris TM3402 eMTA. A Cox employee posted on dslreports.com forum that as of 10/01/2018 the TM3402 is available to everyone on all tiers. This modem was previously only available on the Gigablast tier.
Here's what mine looks like compared to yours. You can obviously see the difference in ms (milliseconds).
Tracing route to youtube.com [172.217.4.174]
over a maximum of 30 hops:
1 4 ms 3 ms 3 ms [192.168.0.1]
2 12 ms 13 ms 11 ms 10.33.0.1
3 13 ms 12 ms 13 ms 100.127.77.28
4 17 ms 17 ms 24 ms 100.120.100.36
5 29 ms 29 ms 30 ms 68.1.4.252
6 29 ms 29 ms 28 ms 72.215.224.173
7 * * * Request timed out.
8 27 ms 26 ms 26 ms 108.170.225.74
9 29 ms 30 ms 27 ms 108.170.234.213
10 30 ms 27 ms 29 ms lax28s01-in-f174.1e100.net [172.217.4.174]
