IMO...I think when Penn starts drilling you with a lot of questions, you simply need to say....Penn I have business to attend to and that is all you need to know. You should also tell her that it's not polite to ask people so many personal questions.
It seems to me that Penn is not getting a lot of attention from her mother. Her mother has brought her a lot of materalistic items to keep her occupied, so she does not have to deal with her. Penn sees the relationship that you have with your daughter and that is something that she probably wants with her mother.
If you invite Penn to the Junior Night, your requirement should be that Penn's mom attends as well. If her Mom can't or won't come than Penn will not be allowed to attend . I know this may sound like Penn is being punished for her mother's actions but it's not fair that you should be left having to care for Penn and her mom is somewhere else doing whatever. I would also remind Penn's mom that if she has to leave early for whatever reason Penn needs to go with her.
You should not have to adjust your schedule to fit Penn's needs. The best way to curb this is to be honest and open with Penn's mom. When she asks you if Penn can spend the night, kindly say no and explain that when Penn comes over she is often bored after a short period of time. Or if you have made plans you shouldn't be apprehensive about saying that you have plans to do whatever that night or the next day. Even if the Mom says she will pick Penn up before your scheduled events continue to be firm and say no, because you really don't want anything interferring with the plans that you have scheduled. If you stand firm on your no's than it is less likely that they will continue to ask if she can come over. Don't keep explaining why Penn can not come over. No means no and they both need to learn to accept it.
One last act of kindness I would try (for the sake of Penn). I would ask the mom if SHE would plan a mother-daughter day out for the four of you. Tell her you will leave all the planning to her and she can let you know what day and where. If you are available to go, tell her you can meet her at the location of choice. Do not get suckered into picking Penn up with the promise that the mom will meet you there. If the mom has to cancel for whatever reason and she tries to insist that the three of you go ahead without her, tell her no and she can reschedule when it's convenient for the four of you to go out.
Be blessed!!