K.
I had a VBAC in June at UIC. I also suggest you contact the ICAN group of Chicago - someone there will certainly know about CDH and/or the doc you recommend. VBACs are safe - all of the evidence shows that the risks are small and the benefits are excellent for mom and baby compared to scheduling a repeat c-section. The only reason they have become less common is that ACOG has taken a risk-averse stance in their policies to avoid any potential litigation. Everything I have read indicates approximately a 0.5% risk of your scar re-opening (and this means a 99.5% chance that everything will be just fine).
VBAC success is highly dependent on how much the mom wants it and how supportive the healthcare provider is. So... if you want one, find someone who is supportive and go for it! Stay healthy during your pregnancy, get a doula, avoid any unnecessary interventions. (This is a compelling reason to opt for a midwife instead of an OB, since midwives are experts at sitting on their hands). Good luck and congrats on the pregnancy!