Hi, it may be useful to talk to an Ed Psych. If they have challenging behaviours at school as well as at home, they may have some underlying medical issue (eg ADHD, Oppositional Defiant Disorder, Conduct Disorder or ASD).
To manage any of these you would have to have superhuman parenting powers. A Child Psychiatrist can help you as a parent but may also suggest medication to stop their brains going at 100 mph.
The Ed Psychologist would be able to suggest teaching styles that would benefit both home and abroad.
I don’t believe in labelling children. However sometimes they need those labels and diagnoses before you can access services.
Think about cutting down your hours if you work. I saw my work as a release from the challenges at home. However, with hindsight I should have cut down my hours because a few more hours at
home would have made it easier to attend the multi-agency meetings and just to have some quiet with a coffe or walk the dog and see some sunshine.
Also, join a parent support group. You are not on your own but you damn well feel like you are and not being able to leave your child with anyone means you are on the go 24/7 and no one can keep up those hours.
Get the help for yourself. You may find you are forever putting your needs and your social life to the back of the queue. No one can sustain that.
Good luck.