Wow - sounds like you are extremely overloaded with multiple tasks.
Working from home has its pros and cons - especially with young children. I assume you have childcare, but it's still a drain on your own head space if you are 'around' all the time.
I frequently work from home, and find that in addition to a million hours working week, I'm also the home 'project manager' - I do have childcare, cleaner, gardener etc., but I have to make sure that it all gets some (unlike my DH who works out of the home) and it makes my head explode sometimes.
Workwise, I would check first to see if you really have too much to do in the allotted time, or if you just have too many threads to follow, which can make you feel suffocated when you're finding your feet in a new area. I can sometimes feel overwhelmed if I have a project(s) that needs me to purely focus on it as an intellectual task, because I can never clear the decks of all the other tasks and get on with it..
To look at things objectively, I'd start by creating a weekly work resource plan with you as the sole resource.. Create a matrix of all your current work regular tasks / responsibilities / activities, plus adhoc projects . Putting it down in a spread sheet or similar should give you a view of all the tasks in one space. Allocate approximately time to each tasks and look at how that corresponds with your working weekly hours.
It might show that you should be able to do all the tasks in your allotted time, if you were already experienced in your role, or if it shows that you can't physically accommodate the work in your working hours (regularly), book some time and go through it with your line manager.
Looks like you need to make your management see that by overloading, you're risking becoming ineffective in all areas or taking time off with stress.
Good luck; you must be very capable to have managed so far xxx