Dear P.,
This is a tough one.
I have been a single mom for years. By choice. It's hard when you have to be away for work and then you come home and there is still so much to do. Your kids are definitely old enough to help with things.
It was like pulling teeth to get my daughter to do anything. Give her a chore and all the sudden she had somthing else that HAD to be done right then! My son is the complete opposite. He not only helps me, but if we go stay with friends or relatives.....he helps them too. He offers to take out the garbage or feed the animals or sweep the porch off.
She's 22 and he just turned 13.
Some kids are helpers and some kids will find any way out of it that they possibly can.
I know you are busy and have your hands full, but one kid should not be taking on the other kids chores because they can't or won't do them.
Be sure you carefully examine the homework your children have as soon as you get home. (Kick your shoes off, get a soda, inspect the homework before you inspect the house. If one kid's is done, check it over. If the other kid's isn't, say you need to look at it and determine how much time it should take. Talk about if it's something that should be taking so long to finish. If there is a lot of research involved or something. Maybe she's being lazy. Maybe she is struggling. Maybe you need to sit her down at the kitchen table as you are cooking dinner so she can have it done in time to help load the dishwasher and clean the kitchen when you are through eating.
This can be worked out, I'm sure. But it really isn't fair to the other kid to have to do what she won't. If she doesn't do her stuff, then, she has to do BOTH kids' chores the next day. And the next day, if she wants to be stubborn. When she has no clean clothes or no clean dishes or a clean towel to take a shower with, she will get the hint. That's what worked with my daughter. In the meantime....constantly praise the kid who helps you all the time. They deserve to hear that and know they are appreciated. Plus, my daughter noticed all the praise her brother was getting. One day she said, "He's your favorite. You love him more than me!" I said, "No, I love you both the same. Perhaps he loves me more than you love me because he never comes up with a reason to get out of sweeping the kitchen floor when it's YOUR turn to do it and you have something else important to do....every single time!"
I know that probably sounds mean, but Gosh darn it.
I don't care how cute she was or how much I loved her, her brother and I were not her slaves.
Best of wishes.
Know exactly what's going on with the homework. Make sure she doesn't have so much because she's not able to finish in class. Check on those things first.
Then, go from there.