Thank you for posting to the Community. It's unfortunate that you are having video quality issues when streaming to the Chromecast. When the video is poor, the main culprit is the network speeds. What are the network speeds at both the home location and the remote location?
How the Slingbox/SlingPlayer and Chromecast work together. The video signal is initiated by SlingPlayer, then handed off to the Chromecast to make a connection with the Slingbox. SlingPlayer also maintains a separate connection with the Slingbox to send IR commands. For the best video quality, make sure that both your mobile device and Chromecast have a good Wi-Fi signal available. Anytime the Wi-Fi signal isn't so good, performance may suffer. Also, you must keep SlingPlayer running in the foreground until it has established a connection with Chromecast. After the connection is established, you can put SlingPlayer in the background by going to another app.
Hope this helps,
Sling Media Moderation Team