Been trying to remember this one and haven't found it despite extensive googling. This was young-adult or magazine anthology fiction about a family that ends up time traveling, but can't get back to their own time easily because of two factors: they are low on energy/fuel and the short jumps paradoxically take more energy than long jumps. They end up traveling all the way to the end of the universe (heat death?) and note that local scientists are trying to solve the problem of how they can exist in a world where the electrons are all disappearing due to decay (i.e. need to come up with a proton-only technology. Did I dream this or was this really a work of fiction I read at some point?
You didn't dream it, it's one of my favorite (not so) short stories: Poul Anderson "Flight to forever", published in Isaac Asimovs "The last man on earth". Despite it's not a family but two scientist who try to get back home.
A Science Fiction novella about a scientist who invents a time travel machine and travels about a hundred years into the future with his assistant but discovers that they can only travel forward in time. They decide to continue travelling forward in hopes that science discovered a way to travel backward in time so they could return home. They keep stopping at various times