Locking a door is not a difficult thing to do.
I suppose that you just need to decide whether you prefer to get up and lock the door, or make stilted and desultory conversation with DSD’s mum every 2nd day.
As an adult, and a stepmother, what you don’t do, is ask DSD to tell her mum anything!
Children know who they belong too.
It can seriously mess with a child’s head when they have one parental figure telling them to give another parental figure messages.
Don’t damage your relationship with your stepdaughter by asking her to tell her mother that she’s not welcome in your house!
To a child, she will hear you saying that she’s not welcome in your house. After all, she is half her mother as well as half her father.
There’s a reason why relationships can become so fractured between parents and offspring when said parents divorce! Because all the offspring hear, when parents can’t control themselves, is how dad is xxx or mum is zzz.
The children get damaged! Sensible parents don’t talk smack about the other parent in front of the children - they keep adult things between the adults.
All this to say, preserve your relationship with your DSD, who is 1) innocent in all this and 2) the sister to your own DC!
This is your DH’s responsibility as he is the father and therefore, it is up to him to talk to the mother.
I would also raise whether it would be better for DSD to be dropped off to school and her mother can collect her from school and the same for when you have her, you collect from school. If this doesn’t work, what about week about instead? Sunday night to Sunday night? 2 days on/off is not going to work so well once your own DC are older, or you decide to return to work, or for a myriad of other reasons that may become clear in the future.