Besides wanting your SD to help out more... what is your HUSBAND doing, daily, per "chores" in the house????
I think, HE can, and should be... doing things too, daily, in the house and per helping his daughter, too.
I have 2 kids who are 6 and 10.
My 10 year old, can do what you want your SD to do.
But I don't have her do it everyday. She gets tons of homework daily and has other after school classes.
My 6 year old, could do those things too, but he is 6 and he gets homework too.
And per my kids, I like for them to also, have downtime. They are in school all day and get homework, and we also like to have a spot of family time, nightly.
I am a SAHM and also work part-time.
I know how you feel.
But for me, depending on the how the day is going, I may have my kids do everything, but never more than they can handle. Or I give them a break. They are mostly good about things, but some days, they are very bogged down with school things and we are busy after school, too. We are not just staying home everyday after school.
Again, I think, your HUSBAND can be and should be, doing more things around the house, too. Not only your SD.
With my kids, I do not make them do the laundry and fold it and change their sheets. I do it. I prefer to do it myself.
My Mom, who lives with us, she herself has a HARD time changing the bedding on her bed... because the mattress is heavy etc. and she has aches.
I think, your SD's daily and weekly chores are fine as it is. And she does seem to clean "her" area.
But, the OTHER thing you can instill in her is: that being a part of the family is NOT just doing things for only your things or only your area... but for the upkeep of the home. Being she lives there too. That is what being a family member is.... HELPING out, in the home, when/if there are other things to do.
My kids have their chores to do, per their age and ability. BUT for me, it can change daily in amount... because, on a daily basis and just per life... sometimes more things need help and on other days, not as much needs to get done. SO I TEACH my kids, that HELPING in the house does not mean, only doing "their" things. Because, if I ask them to do something else in the home to help... I don't want them to tell me "But that's not my job...." I want them to learn... that flexibility is needed, too. Because, life can change everyday and what we as a family, needs to get done.
And I do not expect my kids to be the house "maid." Rather, I teach them to be a PART of the family and home, because THEY are a part of a bigger entity beyond themselves.
Again, why can't your Husband be assigned chores too?
He should be doing something, whether or not he works.
I am a SAHM who works part time, and my Husband works, and HE is expected, to help in the house and with the kids TOO.
He is not off the clock, just because he works and I sort of don't. Being I am part time.
EVERYONE in a family... HELPS in the house and its upkeep. IT IS everyone's... home. That is what I teach my kids, about "chores."
They are not "Cinderella", but they need to help. AND show initiative about it too.