ISO-scheduling software…

I'm am struggling to use a number of options simultaneously to accomplish something that shouldn't be very difficult but is so I need something probably designated especially for me. I run a space (co-work space) that has a gallery, large classroom, conference room, and warehouse. These spaces are scheduled and paid for, if not already booked. The calendar these events post to should be public, real-time, able to embed on website, and connected to our payment program. Currently, every step of the way, someone has to approve each step, we want to eliminate that. Anyone have a direction they can point me in?