One day in BH should be plenty. Pick a great hotel nearby (like the Peninsula) and a great spot for lunch and shop before and after. BH has much more inventory than SCP, for instance there is a whole floor of home. For scarves ask for what you want as they don't display more than a fraction of what is there. Also BH isn't cagey about what's in back except for bags, so if you are looking for a particular scarf design, etc., if they have it they will find it for you.
BH Hermes has parking in back - there is also tons of public parking in Beverly Hills - so I don't agree that parking is more difficult than SCP.
I like the SCP H boutique and that mall is kind of fun (it is nearly all high-end shopping) but it's a small store. It's so close to Anaheim, though, you should stop in. I would not bother with SD.
Both stores suffer from "tourist-itis" - they give preference to locals who will be repeat customers - but for silks and soaps that doesn't matter. Have a great trip!