Have recently built my first weapons emporium at Sanctuary & have put the Vault-Tec Rep in charge. At first all seemed to be going as it should. But now whenever I go to him instead of opening up a big list of weapons, ammo etc my character either starts a trade with him or the shop will be empty with him only having 6 caps. Is this a bug of some sort? Has it happened to anyone else?

They don't trade at night, try movng it to flatter land

Their shops close at night, so when you talk to a vendor after hours it just brings up the normal trade menu. Their stock and caps reset every 24 hours, so if you're selling a lot of stuff to them, you have to wait until it refreshes to sell them more.

Btw.: are you sure that "Vault Tec-Rep" and "Weapons Emporium" are a good match? According to http://fallout.wikia.com/wiki/Fallout_4_merchants he's a General Trading specialist. So, even if he can be assigned to a weapons emporium, I'm not sure whether he will trigger the Lvl 4 items for that shop or not, like Smiling Larry is supposed to.

he won't. on mine, whenever i go to his shop (weapons) he carries on about this and that, and my toon asks him to work for me. i have to wait for him to finish babbling before i can use him. i have rylee on the junk stand, and i'm scared to mess with their assignments, because at least they haven't bugged out completely or disappeared. knock on wood.

Lol yeah. You have to wait till he stops talking about how great it is that you and him are finally together at sanctuary. And don't get me started with Sturges! I asked him to work on the armor stall & at first he did, but later on I find him hammering away on a building! haha. Maybe it was after hours, can't remember.