Question: Is there a life-threatening condition that twins could have that could be fixed with minor surgery in the 1830's?
Answer: This question sets up a very difficult scenario for the author to work through. First conundrum is the "life-threatening", " minor surgery" and "1830's". First of all, most life-threatening conditions require a fairly extensive surgery to fix. One life-threatening option that might easily be fixed would be to have a severed artery that could be tied off. But, this doesn't fit with the twin scenario. Next problem is that surgery wasn't all that advanced in this time period. No OR's... etc.
Secondly, a condition that affects the twins. First thought that came to my mind was a congenital heart defect present in identical twins that would require surgery. But again, limited by the chosen era. Not a good solution.
Then, I thought of the post I did on milk sickness http://www.jordynredwood.com/2011/06/anna-bigsby-milk-sickness.html. A good idea for this time era would actually be a medical condition that the local doctor could figure out and treat. Something along the lines of a toxic plant poison passed through the mother's milk or a metabolic disorder that could be managed by diet. It would take a very crafty doctor to figure out and would be a plausible option given the constraints of that time period. Here's an extensive list: http://emedicine.medscape.com/pediatrics_genetics.
Any other thoughts for this writer?