The 2x4 will fall in with the food and the rat. After eating the food, the rat will climb out using the 2x4 and reposition it on the counter so the dad will put out more food.
I mean, to be fair, bucket traps are a tried and true rodent trapping method, when done right at least lol.
I think with the "walk the plank" style bucket trap he'll need a pivot point further into the bucket so the rat has to get partway across before it'll fall, which prevents it from jumping back before it falls in. Can do this with a thin rod that goes across attached to the bottom of whatever is used for the plank part.
One method that also sometimes works is putting a ramp on the side of the bucket to let the rat up, smearing peanut butter a few inches below the rim on the inside, and then greasing the edges a bit, so the rat has to try and reach in to get the peanut butter and then slips into the bucket because they can't keep a grip on the sides.
Or he can go the Mouse Hunt route and just befriend the rat. I'm sure that couldn't possibly go wrong.
Hello, James. Welcome. Do you like the island? My grandmother had an island. Nothing to boast of. You could walk around it in an hour, but still it was, it was a paradise for us. One summer, we went for a visit and discovered the place had been infested with rats! They'd come on a fishing boat and gorged themselves on coconut. So how do you get rats off an island? Hmm? My grandmother showed me. We buried an oil drum and hinged the lid. Then we wired coconut to the lid as bait and the rats would come for the coconut, and... They would fall into the drum. And after a month, you have trapped all the rats, but what do you do then? Throw the drum into the ocean? Burn it? No. You just leave it and they begin to get hungry. And one by one... They start eating each other, until there are only two left. The two survivors. And then what? Do you kill them? No. You take them and release them into the trees, but now they don't eat coconut anymore. Now, they only eat rat. You have changed their nature.