Hi Tom,
unfortunately I don’t know how to continue here. I am waiting and I hope, that perhaps one of the experts finds this topic. Apparently coupling is difficult according to this thread. However in the power point here, slide 5, something very similar is shown (without full code unfortunately).
Probably you have already found this post but I wasn’t able to solve the coupled domain problem with this.
I have the feeling that I miss something when coupling a whole domain problem with a sub domain problem and I haven’t found an answer in the forum or somewhere else. I guess splitting the whole domain problem to each subdomain and imposing interior boundary conditions with Lagrange multiplier like here might be the solution.
I think it would be great to have an example on this from people much more experienced (or even developing) dolfin / dolfinx, perhaps someone finds the time 
However I really very much appreciate their work and I think its a great tool… Let’s see!