Are you sure she is not using pork or goat? Depending on region in Mexico--if she is being traditional--other meats are used. Goat is very common.
Beef barbacoa (head) is pretty fatty. Typically it's not stringy, though many here (Texas, Calif, elsewhere) do use chuck and its texture is more chuck-like. Netted beef roasts are often rib roasts or top sirloin. Chuck eye would probably be what I would use were I cooking beef and not using the head or the cheeks alone.
I'd use mostly California with just one guajillo. Onion and garlic are musts. Some cooks add jalapeño and tomato during the cooking process (some also flavor with lime juice as well) and others reserve these items for use at serving. Typical seasoning is black pepper, oregano and often but not always, cumin and cinnamon. Bay leaf is often used if the meat is not being wrapped in maguey or banana leaves.
In Mexico barbacoa has smoky notes if it is traditionally cooked, not so much here if it is simply cooked in an oven or Crockpot. You could rub (salt, pepper, garlic, onion, a liitle ground chilie, oregano), smoke till 160s, then either wrap in leaves (and place it in a pan) or in foil, adding your aromatics to the wrapper of choice (reconstituted chiles, shredded, chopped onion, minced garlic, a bay leaf or two, a little cumin, maybe a piece of a cinnamon stick, a good squeeze of lime, some minced jalapeño, a chopped tomato), and cook till fall-apart tender. Then you'd remove the meat and solids from the wrapper, shred the meat, mix with the solids, reheat to tighten a bit, and serve--preferably for breakfast with good tortillas.
Of course, you can use--or not--whatever sutis you in terms of aromatics in the wrapper, saving others to serve fresh alongside rather than cooked with the meat.
What do you have in mind?