Ahh Kitty, it's not easy and you are being awfully hard on yourself and seemed to bearing the load for the whole household.
When the kids get up in the morning, do they make their own beds?
So, you have 3 in School? While they are at school, get a dinner ready during the day for the family.
When the kids come home, get them to do some of the chores, washing dishes whatever they can manage, even if it's just putting the cutlery away.
At 5pm let the little ones have their dinner including DS5 and get the older ones to help out while you get the bath ready and feed Chakotay (he could have had dinner with the little ones and only need a BF to get him to sleep). If you can get your little ones in bed by 7pm, job is half done. Get your DH to sort out DS9 and DS5. Even if the communication lines are down between you and your DH he still has to pull his wait with the kids.
That leaves you quite a bit of time to help DD12 with this project.
If this doesn't suit, let your DH take all the kids for an hour and try and work out something that is going to make things a little easier than they are.
Preparing ahead has always worked for me, and a strict routine.
No-one expects you to be a super mum..do they really exist LOL!
I suppose you could look at it this way, try and get the kids a routine that works around you rather than you have a routine that works around them.

Tonight is Friday...I loooove Friday! I don't cook, kids have a cold plate (takes 5mins to throw it on a plate). Meals can be easy and nutritional. I let the kids watch a movie till bed, no stories, teeth and bed. Friday is what I consider to be my night off.
Think of yourself, you are very important to your family, never doubt that.