Fluxx! Need to be able to count to 5 and match pictures to participate, and the winner is fairly random, so works well with young children (obv avoid the adult sequels like Stoner fluxx and Zombie Fluxx...)
A game where the dice are enclosed in a popper is great - I couldn't believe how difficult it was for ds and dn to roll a die and have it land on the table and then find it. Frustration is the classic with this format, and just pushing the popper to roll the dice is lots of fun.
Dominoes would be good if you get a classic set with the numbers in different colours.
Pictionary is good for all ages if you ditch the board and just have teams where players take it in turns to guess what one of their number is drawing and then the other team get to guess if they don't manage in the time limit.
3 is a bit young for much else other than snakes+ladders or Matching Pairs type games, but if the kids got paired with an adult each, Carcassone and Scotland Yard could work quite well.
SET is a game based on psychological experiments - you need to be able to count to 3, to find sets of 3 cards on the table which have each of 4 characteristics either all the same or all different. Small children are often the best at it.