I don't think I've ever seen a small child at a high-end restaurant in Japan. The only places I see small children are fast food restaurants, family restaurants, and the kinds of general shokudou-type places found inside department stores, which often have an o-ko-san ranchi (children's lunch) featuring kid-friendly foods.
I can't even imagine bringing food from elsewhere into a Japanese restaurant. It would be insulting to the owner. In fact, I can't imagine doing it in the U.S. Think about it. If you went to a high-end seafood restaurant in a Western country, would they appreciate your bringing in a bag from McDonald's for the child? No, you just wouldn't take the child to such a place.
If you must have gourmet sushi, you may have to take turns going, with the other parent staying behind in the hotel room eating a convenience store bento.
Or, if you stay in a couple of ryokan or minshuku or a hotel with a dining room in Hokkaido, you can sample the local seafood without inadvertently insulting the owner. The child can nibble off the acceptable portions of the often lavish in-room spreads that traditional accommodations provide, or you can order off the menu in the hotel dining room, with you enjoying the catch of the day and your son chowing down on something less exotic.