Thanks for reaching out!
I'm not an expert in streaming by any means but I do know that streaming live to twitch or youtube can be quite intensive on your bandwidth. If I had to take a guess I would assume that your ISP is the bottleneck for your bandwidth and not your home router. With that said you can try reaching out to them to see if you can upgrade to more bandwidth/speed and that could help with the issues are experiencing when streaming.
For more about bandwidth saturation you may find the following article insightful: Bandwidth Saturation
In regards to your PingPlotter screenshots you shared, the packet loss you have observed at the first hop is a bit of a red herring. Some routers just don't prioritize timed out ICMP requests very high (ICMP requests where the TTL equals 0 after reaching them) and this is the case with your router.
If you run a trace directly to your router (192.168.1.1) it should prioritize these packets better and show little to no packet loss. You can read more about this in the following article: One Poorly Responding Router
Another very important takeaway from the article above is that the most important hop in your trace is the final hop, if the results at the destination look good (acceptable latency and minimal/no packet loss) then everything that comes before it can be ignored.
In this case, due to the nature of screenshots, it is difficult to say where the packet loss that does carry through to the final hop originates. If you look through the following articles about interpretation you can get a better idea of where the issue could be starting while looking at your results. Interpreting PingPlotter Results Interpreting Latency and Packet Loss
With that said it looks like you are using the free version of PingPlotter. When trying to troubleshoot a network issue the more data you can collect the easier it is to figure out. We do have a product called SideKick that helps you gather the data, interpret it, and help you know what to do next. Plus, it makes it really easy to share your data with other parties like your ISP.
The best part is that it's only $20.00 USD, which I think is a pretty great deal for diagnosing where your internet issues are. You certainly can't get a tech to come out and tell you were the issue is for anywhere near that amount!
SideKick is a temporary license that lasts for 28 days - which we've found to generally be plenty of time to isolate a network issue. If you're stumped or don't get a definitive result feel free to send us your data and we'll be happy to take a look at it and give you our two-cents.
You can learn more about, or purchase, SideKick using the following link: PingPlotter Sidekick
If you have any questions about this let me know!