I have a 5-year-old boy, with two younger brothers (1 year and 3 years old). He is intelligent, sensitive (easily stressed) and shy. I would definitely label him an introvert, but he does not like to be on his own and has issues when someone leaves (e.g. one of us parents).
He can be super kind and loving to us and his brothers, but often he is not. Multiple times a day he can get hostile at us or his 3-year-old brother (insulting and sometimes even attacking physically) for the smallest things not being as he wants or as he expected them to be. We try to stay calm and kind (of course, we mess up sometimes and get angry, but not very often). I struggle to handle the physical attacks when he gets into a fury, keeps attacking and won't stop. It usually ends after a while when he gets hurt (unintentionally!) by one of my defensive moves and starts crying and blaming me for hurting him. I don't know how to stop him before. He won't react to any words at this stage. I usually stay calm.
We try to spend time with him alone, without his brothers. This mostly works, but of course, the time we can give is limited. He likes sports, but is easily frustrated (e.g. for not catching a ball) and always wants to play against others while getting angry if he is not clearly winning. And every few days he has nightmares in his sleep.
From watching him closely I think he is mentally exhausted from the time at the kindergarten, being with friends or simply with us and/or his brothers. Something I as an introvert can relate to very well. But he is lacking a proper way to relax through the day. He actively refuses to do something on his own and has a hard time to busy himself. We have several toys great for playing alone, many books, a music player with audiobooks, a place with a lot of stuff to do handicraft work and many other possibilities. But he always wants someone to be with him and additionally seeks activities frustrating him (e.g. playing against others, crafting a perfect paper plane).
What can I do to help him relax on his own and develop some resilience?
Edit: I just had the yearly talk at the kindergarten, he is like the perfect child there. He plays with everyone, shares, solves conflicts, has a sense of the needs of others. He cares for himself and can do things on his own.