My mom lives in a pre-1900 house with add-ons built in the 1940's. The plumbing was added sometime after the 1940s additions. The kitchen sink when she moved in was from the 50s. The plumber she hired just scratched his head and did patch-up jobs, and the plumbers she's called since don't want to touch it due to its age. This winter was the final straw as the temps dropped low enough that the pipe that passes through the old stone foundation cracked (looks like the crack may have been there some time as there was old electrical tape wrapped around the junction from iron pipe to pvc).

What I'm looking to do is just remove out the sink she had installed, and replace it with a single drain sink (she doesn't have a disposal, and for some time when she'd try and plunge the one sink the waste water would just pass to the next sink). Where I'm stumped is the pipe in the foundation. What is the best method to replace something like that?
Thanks for any help.