Is it my problem if the store will be super understaff when I leave?

They can't make you stay. Really, if you stop showing up at work, are they going to come to your house and drag you back to work? They also can't keep your last paycheck. They must pay you for whatever you worked. Therefore, there is nothing they can use to force you to stay on the job.

But don't count on using anyone as a reference for future jobs.

she can't not let you quit? it's illegal, if you want to quit you have every right to do so. she CAN refuse to give you a good reference.

no it's not your problem. Doesn't let you quit? You don't need her permission. You give notice saying when your last day is, then remind her about a week before your last day. If she schedules you after that, remind her again that you won't be in after {date}. If she keeps you on the schedule, you just don't go.