There is no reason whatsoever for her to nurse in the daycare. She lives a few minutes away. She can nurse before she drops off and right when she gets back home. She just wants to hang out at your house so she gets more time in the daycare. She is doing it because she doesn't want to be alone with her kid any more than she has to and she likes hanging out to watch you work. She wants attention for free.

Tell her it isn't working and that you will have her child ready to scoot out the door quickly when she arrives to pick up and will greet her quickly at the door at drop off so she can hurry off to work.