OP, since it is almost summer, I am sure that you can find something that will work out with the days you have available. There are lots of kids that will be in camp and have parents that can try and pick them up after work, BUT might find it more convenient to have someone help and pick the kids up for them a few days a week. See if you can find one that the parents wouldn't mind having a late evening, so you can get more hours. They can work late those days to make up for their rushing from work the other days. They can have a date night. Look for regular weekend babysitting. You can make it this way until fall, when you then switch to a FT position instead.
You might need to watch your finances a bit more during this time, only pay bills and and very little other spending, but it should work.
I work about 20-22 hours only in San Francisco, and I not only manage to live on that, but I have been saving up over the past couple months for summer since I don't know what other PT work I will get (I have a live-in exchange so I am covered with rent, but need to pay for food and other basic bills). I have saved up to not work for anyone else if needed (or wanted), but that is more of a backup plan. Anything I do earn this summer will be pure spending money (or savings).