I have two thoughts:
1) Woman up. Grow some ovaries and occasionally have an uncomfortable conversation. Be kind about it, but be an employer. Do you really want your children to learn to avoid challenges like that?
2) The one babysitter I fired without a conversation was the one who sat outside on a concrete patio on a sofa with my 9-month old son. She did not have a hand on him, and was looking at her phone, which she had been on the entire day. I was here, and I told her that he wasn't able to get up and down yet, and could fall and get badly hurt. Ten minutes later, she was doing it again. I decided she had terrible judgment.
One other thing. I found out that our nanny was driving the kids short distances without buckling them in their car seats (as in, they would go to the park next to the library, then drive around the building to the library). I was horrified, but my kids were old enough to tell me what was going on, and she never did it again. She's been with us for 2.5 years. I knew that she was generally very careful with the kids and I do trust her judgment. This was just something she was raised with in a less strict way, and she was happy to correct it. You would have fired her, I guess?