How do I fix cracked plumbing in this situation?
PVC is pretty simple to work with as long as it fits well. I'd cut off the broken elbow cleanly and leaving just enough protruding from the stack tee to connect a new elbow, say 3/4". I'd clean it up and prime it and install a new standard elbow (is that a 45?) onto the stub. Give a twist to distribute the cement well. You many need to cut back, and then extend with a coupler, the straight section. 

Another option is to cut the elbow off, then carefully grind away the portion that remains inside the stack tee. If you work slowly with a rotary grinder, checking fit often, you should be able to make a new street elbow fit well. Prime it and cement it in, rotating at least 1/4 to distribute the cement.

Because this is an unfinished area, risk is low if the new connections fail. At that point you may want to get a plumber in to replace the stack tee and start fresh.