Here is how you fish to get the cat to run inside to the shop lady.
All you need to do is assign the pole to the b button. Push the b button so the pole is out. Then fling the wiimote foward or just kind of drop it down so your line goes in the water. This first fishing pole is a simple pole, meaning it has no reel. So you just let bobber sit in the water until you see it get taken completely underwater, at which point you yank the wiimote up/backwards like you are hooking a fish, and just hold that until you bring the fish in. You have to actually catch 2 fish for the cat part, because you will release the first one and the second one will drop on th dock near the cat.