Have you reached out to the tomorrow.io team to see if they have any suggestions on how to make their widget auto refresh? It looks like the main thing their script is doing is injecting their own iframe, so I suspect you could grab the URL for that and use it in a Refreshable iFrame Custom Tile.
For example, the Weather Widget with Upcoming Days for Brampton, ON, CA looks like a URL of:
The community enforces some restrictions on new accounts to prevent spam. Normally you level up automatically over time and the community increases your trust level. In the meantime, I’ve manually bumped up your community trust level. 