Temper tantrums

Help!!! I babysit a girl who is almost 2, and I have my own who is 4 months. This toddler, every hour almost, has temper tantrums. Sometimes over nothing at all! She just shrieks at the top of her lungs and I am not her mother so I cannot punish or discipline her, and she doesn't respond to me well at all. She does not listen. And now it's affecting my baby and she can't take naps with this girl SCREAMING. I need advice because I'm trying to help out this poor mom, and I don't wanna have to turn her away, but I don't think I can take this much longer.