Active Directory / DNS naming design, multiple sites, single domain,
Solution 1:
You don't have different DNS namespaces for the two branches if they're in the same AD domain. There's no reason to. They would both be in the same DNS namespace as the parent. What reason would you have for two different DNS namespaces?
Also, avoid naming your AD domain "company.com" if that's also what your external website's name is. Name it something like "ad.company.com" or "internal.company.com". Having a split namespace will cause headaches.