Can I replace a shower door that has one edge joining with another glass pane?
I have never seen replacement doors at a place like Home Depot. Your situation looks like a custom made unit.  You probably will have to have it looked at by a local glass contractor/supplier to see if they can make a replacement door or hinge set up for ya. Unless you can actually find the make and model of what you have now, I doubt you will find a simple off the shelf replacement.