I come from a cultural background where what you have said would also apply. I understand the challenges in you moving out and what that might signal to the full family and her having to then own up to what she did.
So, in this case, what are some steps that you can take for yourself right now? If moving out might not be the most optimal option, then what can you do?
Can you still start your own business and start living your life while remaining in the same house? A new business is easier to explain to the rest of the family.
I am not a supporter of an in house separation, but in your case with the added cultural context, it might make sense to do that. But, if you decide that route, you have to truly live your life and not give a f#ck what she does. You have to really DB and not look back. But again, this will be a temporary solution and I would put a time limit on it. Ultimately you will have to move out if things don't change and then you might be in a better place to explain to the rest of the family.
So, the question is not what will bring your W back right now. The question is, what are you comfortable with at the moment? She will have to face embarrassment at some point with the family - either it's now or it's later.
The answer should come from what will bring you peace and a better state of mind. Not whether that this decision will affect her or not. Actions have consequences and she needs to feel the impact of those consequences.
Make the decision for you, not what will be easier for her.
