People can (and will) try all sorts of things. They'll try to get free babysitting, free carpool rides, free help. They'll try to be dishonest or rude or any one of a number of things.
You can't always change that or have influence over it or control it.
What you CAN change, and what you can control, is your response to rudeness or manipulation.
Why do you say "sure" when you pretty much know that it's not a playdate, it's free babysitting? Why do you hide behind your door or not respond to texts?
If Mary is ringing your doorbell, with her mom in the car, you open your door, you take Mary by the hand, and you lead her to the car, open the door and help her get in. Politely. Calmly.
If Mary's mom texts you, you simply text back "I'm working now and am not available. Sorry".
If it's a nice day and your daughter is outside, and Mary comes over, fine. When it's time to call your daughter in, you do so, and you politely tell Mary to go home.
Getting angry is not doing anyone any good. Be in control of your own situation and your own home, and be clear to the mom about what you will and will not allow.