What do you do if someone in your family is having a bad day? Should you just ignore them? Should you do your best to turn their day around? Should you live through their pain as if it were yours?
Usually, if you encountered negative people, I'd tell you just to drop them and do your thing without them. But family is different. Caring for them is part of the job you agreed to when you chose them to be your family. Ignoring them would be incredibly cold and could make them resent you and leave you. But you can't force them to have a good day, either. And I don't think they would want you to waste your day by taking on half of their suffering - because most likely you're not making anything better by pouting away the day.
So what's the solution?
To offer to console them / distract their thoughts / listen to their worries when you're spending time together, and when you're apart, focus on making your own day as good as possible.
Spending your alone time worrying about someone else is hardly productive. It doesn't help the person, and more likely you'll end up having a bad day, too - which, in turn, easily latches onto them later, even if they have managed to solve their bad day on their own in the meantime.
Furthermore, when you focus on having a good day, and you reach a state of great mood during your alone time, this positivity could latch onto the person as well, even if they hadn't managed to solve their bad mood during the day.
While this sounds like you should always concentrate on your own good mood and try to spread it to others, I don't mean that you shouldn't allow your family members to have a bad day. You absolutely should console them, hold them, listen to what's on their mind, and offer solutions. That, actually, sounds like a solid and active idea that helps. What I am against is needless worry that contaminates every aspect of your day.
You have absolute power over how your day turns out. Make the most out of that.
It'll have ripple effects.