I have a basement shower that does not drain quickly enough, and I am guessing it is due to my vent configuration.

The shower uses 2" plastic piping with trap, which then connects to 1 1/2" copper piping. That pipe connects to another copper pipe which is connected to the kitchen and laundry on the incoming end, and connects directly to the main stack. The vent is connected to that pipe, plus an additional pipe on the stack.

Hopefully the diagram attached explains the configuration.

I have heard the 1 1/2" is enough for a full pressure shower, so that leads me to believe the issue is either with venting, or with my drain being clogged. Does the venting look correct in the diagram?

The shower is wet vented so there's nothing more to be done there. This would fly in my area. Have you snaked the shower drain? What bothers me is while your 1 1/2" branch will handle 3 fixture units, ( a shower is 2 FU), you are jamming 8 fixture uvits , 10 FU if you have a dishwasher, into a drain line rated at 3 FU. To add to the problem you are discharging a kitchen sink, with all the grease and garbage, plus a washer with all that grease and fiber past the lowest fixture in your house that's been choked down one half pipe size. This is recipe for future clogs in my book. But good luck anyhow. I hope it works out just great. Regards, Tom