If you can't come to a shared, consistent view on how to parent your sons, you are not giving them what they deserve. If I thought you were just talking about a difference in style ( like your wife is a little more humorous than you when she disciplines the boys) I wouldn't be concerned. But your letter suggests a fundamental difference in what you both expect from them as members of your family and how you treat them as human beings. I appreciate your attempts to understand your wife's behavior through her own family's dysfunctionality; that shows you're more interested in understanding her and changing the pattern than you are in blaming her and perpetuating he pattern.
Could you use that same non-blaming attitude and suggest to her that you see a family therapist together so that your sons and the both of you can live a happier, healthier family life? Don't present it as her problem; present it as a family problem that you two need some help with. If you can get her to agree to go, based on this not being about "ganging up "on her in a therapist's office but about everyone being happier, you may also raise the issue of how difficult it is for your sons to be the siblings of a Down Syndrome sister. Your sons may be harboring a lot of guilt and anger regarding their sister and how she is treated in the family; it would be wonderful if they could find an objective, supportive forum to discuss these and other difficulties they're having. If all this does not and cannot come to pass, you need to seek out help for yourself and your sons. Good luck.