I think it’s great that you want to take this chance to grow in virtue! I think you will probably be much better able to do so if you can get some order into what you are doing.
You say your siblings are 3, 6, 8, and 10. And then there’s you. What I think you need to do is to think outside the box–the 3-yo needs probably almost constant supervision at this point, but he does take naps.
Consider what’s going on with the youngest (whom I will call him). Is he most able to play quietly by himself in the early morning, late morning, just after his nap? When does he need some running around outside time? Etc. He will be much more peaceful if he’s on a schedule that meets his needs.
At a time when he is able to play quietly by himself at one end of the room is a time when you can help the others as they need help. The other time for that will be when the youngest takes a nap. Other than that, you may have to be firm and not work with them too much, because you yourself need to get some schoolwork done!
See which of the older children will be best suited for playing with the youngest at times whne that is needed. For instance, I found that my oldest and youngest did chores together really well, but my two youngest played together the best; see how those things work out in your family.
Also see when the two youngest quarrel the most: a certain time of day? While you are trying to get something done in the kitchen? When they are playing together more than a certain amount of time? Etc. I found that mine would break out into a fight several minutes after starting to laugh somewhat wildly, so I always broke in when I heard that.
So, have one of your siblings watch/play with the 3 yo for a while and then switch so another child is watching/playing with the 3yo. Have the 6yo watch/play with the 3yo doing things where they don’t end up fighting, which may be something like playing with playdoh at the kitchen table while you make lunch.
Have activities planned for the times when each is watching the 3yo: playdoh, playing outside, playing with cars or dolls, etc.
I know this probably seems like a lot of organizing, and it is, but it will help in the long run. Your siblings will be either working on schoolwork or watching/playing with the youngest, and hopefully you will have a bit of time to get your schoolwork done!
I hope all goes well with you during this time of transition for your family!