Quoting Naturally Alternative~19w:" You could ask her to schedule an evening/weekend/off day to meet and greet with her mother so you parents ... [snip!] ... comfortable. After meeting the mother, you can decide if you trust her with the kids or not, and move forward accordingly."
That's a great idea.
Do I know all of the teachers at DD's preschool personally? Hell no. I went to meet them and made my decision from there. When there's a new teacher there, I go introduce myself.
I don't think it's that big of a deal, but OP-- you're the parent. If you're not comfortable with it, do something. Either talk to her, meet her mom, or take your kids elsewhere.