Nikkah only cases take a long time to process .. they question why only nikkah and no rukhsakti? on top of that, the girl is older than your brother and 2nd marriage .. all red flags ..
Solution? Rukhsakti .. a small honey moon .. take lots of pictures .. save receipts of every hotel, etc they go to and places they visit .. if they go out for dinner, lunch, etc .. take pictures ..
yes 2 weeks are less, but you can do a lot in 14 days .. plan it out .. every min of that stay ..
after the girl leaves, start saving whatsapp communication chats .. save call logs .. take pictures while on the phone (screen shots) .. this will be your communication proof that your brother will need to attach to the application .. there is a whole list of what needs to be attached ..download the forms and start going through them .. there is a checklist .. that tells a lot in detail .. if you don't understand something, then ask here ..
my post should help you get started atleast .