Speed is likely to be the issue I suspect.
What's it like when you do catchup with iPlayer or the like & are you viewing in HD or SD?
Watching iPlayer/youtube/twitch etc is absolutely fine, I can watch YouTube videos on 1080p without any issues. I can even stream BT Sport online without any issues. I really have trouble with the YouView box at peak times though (evenings and weekends).
I've ran the diagnostics suggested above and the results are:
Download Speed (Mbps): 9.96
Upload Speed (Mbps): 0.94
Ping Latency (ms): 34.63
Is there anything that can be done to improve the picture quality? BT Sport is virtually unwatchable.
The fact you mention it's bad at peak times suggests that there's probably a congestion problem & until BT/OpenReach do something about that then there isn't much you can do.
I think you'll find that the Youview box uses a higher bitrate for the internet channels , like BT sport , than iPlayer or streaming to your PC so you're more likely to see the problem on the Youview box.