This seems to be a gender split decision. Moms are more likely to opt to be there, Dads are more likely to suggest to do it alone.
It reminds me of the difference between moms and dads changing those incredible all body poops that newborns have. The mom will eek at the muck going up the baby's back, clean the baby, and rinse the offending muck off the outfit and prepare it to be sanitized and cleaned. Dads will howl at the mess, clean the baby up and throw the outfit in the garbage along with the diaper.
Telling the kids is messy.. very messy.. full of intense emotions. The amount of trepidation a parent might feel is nothing compared to the shock, hurt and devastation the children will experience.
You're a surgeon. Do you operate without an anesthesiologist, safe environment, sterilized tools?
In a case as distorted as yours.. talk to the therapist about your real concerns, about what IS the best way to approach this considering the history of histrionics by the mother. Doing it with the help of a professional might be the only way the two of you can work it out.... to choose what works best for all.
You've lived through hell, and it still will be hell. And Bill is right, the toughest impact will be the kids not having you daily in their lives.