I would like to have it so my phone has do not disturb on at night, and then have it turn on later in the day as well. As far as I know, you can only set up one schedule in settings. Is there an app/something else that would allow me to do this?
You could use bedtime in DND for night and the scheduled DND for the daytime. See in Do Not Disturb settings -> Scheduled for enabling Bedtime and then go to clock app for setting its time. This solves night. For day, use the scheduled feature.