You should be getting what you pay for. The average childcare cost per day, aside from discounts, is $22 per day for each child. And that's for a day that starts at 7:30am and ends at 5:30 pm with federally supervised and funded prepared meals included.
Evening care and sick child care (believe it) should cost a little more. But something to weigh is that you are not hiring an educated professional child care provider who will facilitate learning activities and has a wealth (literally) of tools, toys, and equipment. You are hiring a baby sitter. So, weigh the "evening care" issue with the "baby sitter" issue.
I think that anywhere between $30-$50 per night would be fair. I would pay more if she was going to prepare dinner, evening snacks, and attentively participate with the kids the entire time. I would pay less if she's going to just be an adult presence while they entertain themselves or sleep.
Something else to think about are teenagers rather than a collage student. Some are so happy to just get out of the house, make a little bit of money, and they still play like kids. It seems like the younger teens will really enjoy playing with the kids, but the older ones hang out on the cell phones only to be interrupted by the kids. My judgement (may be wrong?).
My pastor shared a story about his family's teen babysitter. He asked her one night, "How much do we owe you?" She said, "Whatever you think I'm worth." He tipped her big time. And she was there baby sitter for a long time no matter how much they were able to pay or not pay. She just loved being with and playing with the kids (worth more than gold) and she loved being a part of their family.
That's the kind of relationship I'd like to strike with a babysitter. My children deserve it. So, in all of your decision making I encourage you to pray. Pray that God would bring the right precious heart into your life, or make you aware of one that's already there, that will connect with your family and children to serve, support, and edify you all in this capacity. God is capable of bringing someone to light and if he does so, he is also capable of providing the funds (of whatever amount they are worth) to be a blessing back to that person.
God bless you in this; it's important. You're already being very thoughtful about it. I encourage you to be prayerful too.