I am constantly short on sinew since I'm upgrading my bow a lot and the only place I can find it consistently is from shops. When and how does the shop reset its inventory so I can go and buy more sinew?
Restocking is based on the game's need to stock equipment to be closest to your main character's highest level.
For example, when the first of your main characters hits level 8, stores are flagged to restock with level 8 equipment. When your other main character hits level 8, the stores are not flagged to restock.
When flagged to restock, the restock doesn't actually happen until you open the bartering dialogue. If you're worried about finding a sinew or other legendary equipment, you can save before opening the new store dialogue. If the restocked items are not what you want, reload and then open the barter dialogue again to see different restocked items.