Does the estimated cost of this plumbing repair seem excessive?
I would never, under any circumstance allow someone to tunnel under my house.  Anyone in proposing this is a complete moron.  It's a drain pipe that is probably 6-10 inches wide.  

The normal solution - which I have done 20+ times for clay pipes in my area - is to break apart the concrete above the drain pipe, dig it out, replace.  While we are inside we try to replace the drain line about 2 feet to the outside... this part is a b*tch - but point is digging up some home right by the foundation on the outside presents problems too.

If the first floor or basement is finished then you have to pull up carpet, go through tile, pull up wood floors - do whatever you need to do.  On the wall you might have to remove small sections temporarily.  

So costs:


Digging 3 foot wide section above drain + kitchen area (not sure what the scope is there).  This can be done by two day laborers and a jackhammer in one day.  Let's say high end $800 - I will give you price that guys would be smiling about after in my area.
bin to throw away trash/concrete - $300
removal of walls (maybe just bottoms) - $500
actual plumbing work - 2K-3K
backfill of area and concrete work - 1-1.5K
flooring??? that is the big question - somewhere between $200 (carpet) and 4-5K
redoing walls - this depends too on how many and what the layout is - $500-3k


On low end maybe 8K and high end 15K.  And when I say low end that is a high first bid that would make contractor happy and 15K is spending a lot of flooring and wall finishes. I just replaced an old clay drain from last remodel.  This city let me do my own plumbing (some do some don't), the city had 3 inspection checks, I paid a crew for excavation and concrete work (I did nothing hard), it took 4 days, and costs me right at 3K for permits, materials, and crew.  We had to go about 50 feet from main stack to exit point - through two walls and a finished basement (carpet).

Now I want to mention something else that is becoming more popular in our area yet I have not used it because of costs.  There is technology where they can run a sleeve inside of existing pipes that creates a permanent solution.  I have been quoted around 8-10K for these and they just didn't make sense for the money because we can do it cheaper - in my area it is all basement so there usually isn't much cost beyond concrete removal and repair.  I am sure someone else on here can weigh in on this.

Another thing to think about too... Is if you are going to have this kind of work done I would really think hard about what else is under your house and do you need any other work done.  If you have electrical, other plumbing, hvac, whatever under there really think if you see any need to change or upgrade anything.  You don't want to do this every 5-10 years and once you get the process going, doing something extra now will be a fraction of the cost in the future.