For 3 year olds I would stick with peanut butter and jelly, maybe pimento cheese and more kid friendly things. Tuna, corned beef is not that kid friendly. Fine for adults but you ave to think on a 3 year olds level.
Serve sweet tea & Apple juice, clear grape juice. PBJ sandwiches cut in different shapes, have fruit with marshmallow cream and cream cheese mixed together (it's so good), have cup cakes and let them decorate their own. Kids are kids and they'll love anything a mommy serves. As far as finger sandwiches maybe make some mini grilled cheeses. Put ham in some of them or something.