Even if it seems hopeless with one hurdle after another, you just gotta take on step forward after the next step, and before you know it, you'll be sprinting, and then jogging at a steady pace.
Besides, he's been lifting those huge logs that would be impossible for most people unless they had a second person to help, so he should be fine with manual labour day jobs, in my opinion.
As for the daughter...she really doesn't seem to understand the situation they're in. I don't blame the dad for yelling, sometimes its necessary to put your foot down. It's the father's job to be stern after all, and vice versa the mother's job to be the compassionate one to balance things out. This isn't a situation where if you give in too much to your kid's demands, they'll simply throw a temper tantrum and forget about it a day later...no, it's a matter of literal life and death with one wrong move being game over.
That being said, I think the parents should have done a better job at explaining how dire their situation is and why they fled in the first place. Just being vague that it's dangerous to go out isn't going to help, because she thinks the brother can handle anything as kids often put their idols on pedestals (sometimes even up until they reach adulthood). They should have explained exactly why it's dangerous outside, where if monsters outnumber the brother or are stronger than him, even he will die (while pointing to that time he almost died from poisoning as an example, and absolutely would have died had the doctor not be in the area), and that was why they all ran away from the previous invasion horde. I guess this is the reason why so many fables with monsters exist, to try and better help younger children understand moral lessons.